Exhibit 4.2

REGISTRATION RIGHTS AGREEMENT

This REGISTRATION RIGHTS AGREEMENT, dated as of January 27, 2017 (this “Agreement”), is by and among Approach Resources Inc., a Delaware corporation (the “Company”), and each of Wilks Brothers, LLC and SDW Investments, LLC (collectively, the “Holders”, and each, a “Holder”).

RECITALS

WHEREAS, on January 27, 2017, the Holders acquired the number of shares of common stock, par value $0.01 per share, of the Company (the “Company Common Stock”) set forth on Schedule A pursuant to the Exchange Agreement, dated November 2, 2016, by and between the Company and the Holders (the “Exchange Agreement”); and

WHEREAS, resales by a Holder of the Company Common Stock may be required to be registered under the Securities Act and applicable state securities laws, depending upon the status of such Holder or the intended method of distribution of the Company Common Stock.

NOW, THEREFORE, in consideration of the premises, mutual covenants and agreements hereinafter contained and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

ARTICLE I—REGISTRATION RIGHTS

1.1 Demand Registration.

(a) From and after the one (1) year anniversary following the Closing, and subject to Section 1.1(b), Section 1.1(c) and Section 2.3, upon written request from a Holder requesting that the Company effect the registration under the Securities Act of all or part of the Registrable Securities held by such Holder, which notice may be delivered at any time after such one (1) year anniversary and which notice shall specify the intended method or methods of disposition of such Registrable Securities (“Registration Request Notice”), unless such Registrable Securities are included in a currently effective Registration Statement permitting the resale of such Registrable Securities in the manner contemplated by the Registration Request Notice, the Company will use its commercially reasonable efforts to file the appropriate Registration Statement under the Securities Act with the SEC as promptly as reasonably practicable after receipt of the Registration Request Notice and, as promptly as reasonably practicable following such Registration Request Notice, cause such Registration Statement to be declared effective by the SEC and to permit the disposition of such Registrable Securities in accordance with the intended method or methods of disposition stated in such Registration Request Notice. The Company shall not be required to maintain the effectiveness of such Registration Statement beyond the earlier to occur of (i) one hundred twenty (120) days after the effective date thereof and (ii) consummation of the distribution by Holder of the Registrable Securities included in such Registration Statement (such period, the “Effectiveness Period”).

(b) Notwithstanding Section 1.1(a), if the Company previously shall have caused a Registration Statement to be declared effective by the SEC with respect to the Registrable Securities, the Company shall not be required to cause a subsequent Registration Statement to be declared effective by the SEC pursuant to this Section 1.1 until a period of one hundred twenty (120) days shall have elapsed from the effective date of the most recent such previous registration.

(c) Notwithstanding Section 1.1(a), the Company shall not be required to effect (i) more than two (2) registrations pursuant to this Section 1.1 in any twelve (12) consecutive month period or (ii) a registration of Registrable Securities, the fair market value of which on the date of receipt by the Company of the Registration Request Notice is less than twenty million dollars ($20,000,000).

1.2 Piggyback Registration.

(a) If at any time the Company proposes to register any of its equity securities (other than pursuant to an Excluded Registration) under the Securities Act for sale to the public (whether for the account of the Company or the account of any securityholder of the Company) and the form of Registration Statement to be used permits the registration of Registrable Securities, the Company shall give prompt written notice to each Holder (which notice shall be given not less than fifteen (15) days prior to the anticipated filing date), which notice shall offer each Holder the opportunity to include any or all of its Registrable Securities in such Registration Statement, subject to the limitations contained in Section 1.2(b) hereof. If a Holder (in such capacity, a “Participating Holder”) desires to have its Registrable Securities included in such Registration Statement, it shall so advise the Company in writing (stating the number of shares desired to be registered) within ten (10) days after the date of such notice from the Company. Each Holder shall have the right to withdraw such Holder’s request for inclusion of Holder’s Registrable Securities in any registration statement pursuant to this Section 1.2(a) by giving written notice to the Company of such withdrawal. Subject to Section 1.2(b) below, the Company shall use commercially reasonable efforts to include in such Registration Statement all such Registrable Securities so requested to be included therein; provided, however, that the Company may at any time and in its sole and absolute discretion withdraw or cease proceeding with any such registration if it shall at the same time withdraw or cease proceeding with the registration of all other equity securities originally proposed to be registered. The Company shall not be required to maintain the effectiveness of such Registration Statement beyond the Effectiveness Period.

(b) If a nationally recognized independent investment banking firm selected by the Company to act as lead underwriter in connection with the public offering of securities under this Section 1.2 advises the Company that the inclusion of the Registrable Securities requested to be included in the Registration Statement pursuant to Section 1.2(a) will materially and adversely affect the price or success of such offering (a “Material Adverse Effect”), the Company will be obligated to include in the Registration Statement (after registering all such shares for its own account), as to each Participating Holder, only a portion of the shares such Participating Holder has requested be registered equal to the product of: (i) the ratio which such Participating Holder’s requested shares bears to the total number of shares requested to be included in such Registration Statement subject to Section 1.2(a) by all Persons (including the Participating Holder) who have requested (pursuant to contractual registration rights) that their shares be included in such Registration Statement; and (ii) the maximum number of Registrable Securities that such lead underwriter advises may be sold in an offering covered by the Registration Statement without a Material Adverse Effect. If, as a result of the provisions of this Section 1.2(b), the Participating Holder shall not be entitled to include all Registrable Securities in a registration that the Participating Holder has requested to be so included, the Participating Holder may withdraw such its request to include Registrable Securities in such Registration Statement by giving written notice to the Company of such withdrawal.

1.3 Expenses. The Company shall bear all Registration Expenses in connection with any Registration Statement pursuant to this Article I, whether or not such Registration Statement becomes effective; provided, however, that if a Holder requests a registration pursuant to Section 1.1 and subsequently withdraws its request, then such Holder shall either pay all Registration Expenses incurred in connection with such registration or such registration will count as a registration for purposes of Section 1.1(c) and such Holder shall not have the right to request another registration pursuant to Section 1.1 during the subsequent ninety (90) days, unless the withdrawal of such request is the result of facts or circumstances relating to the Company or the Company Common Stock that arise after the date on which such request was made and would have a material adverse effect on the offering of the Registrable Securities.

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1.4 Company Purchase Option. Notwithstanding the terms of this Agreement, if at any time a Holder requests any Registrable Securities be included in a registration statement pursuant to this Agreement and at such time securities of the same class or series as the Registrable Securities are traded on a national securities exchange or trading system or any other recognized quotation system which regularly provides quotes on such securities (a “Trading Forum”), the Company shall have the right and option, in its sole discretion, to, in lieu of including such Registrable Securities in such Registration Statement, purchase all or any portion of such Registrable Securities requested to be included in such Registration Statement at the closing or last sales price of such security reported by such Trading Forum on the date of Holder’s request for inclusion of such Registrable Securities in such Registration Statement is received by the Company, or, if there is no such reported quote for such date on any Trading Forum, the last reported closing or sales price, as applicable, of such security by a Trading Forum.

ARTICLE II—PROCEDURES

2.1 Underwriting.

(a) For so long as a Holder holds Registrable Securities, such Holder may request by giving written notice (an “Underwriting Request”) to the Company that an offering permitted under Section 1.1(a) shall be in the form of an underwritten offering (each, an “Underwritten Offering”); provided, however, that in the case of each such Underwritten Offering, such Holder will be entitled to make such demand only if the proceeds from the sale of Registrable Securities in the offering (before the deduction of underwriting discounts) is reasonably expected to exceed, in the aggregate, twenty million dollars ($20,000,000); provided, further that the Company shall not be obligated to effect more than two (2) Underwritten Offerings during any twelve (12) consecutive month period and shall not be obligated to effect an Underwritten Offering within one hundred twenty (120) days after the pricing of a previous Underwritten Offering.

(b) All Underwriting Requests shall specify the approximate number of Registrable Securities to be sold in the Underwritten Offering and the expected price range (net of underwriting discounts and commissions) of such Underwritten Offering.

(c) With respect to any such Underwritten Offering, the Holder making the request shall select an investment banking firm of international standing to be the managing underwriter for the offering, which firm shall be reasonably acceptable to the Company. The Company will enter into and perform its obligations under an underwriting agreement with the underwriters for such Underwritten Offering, such agreement to contain such representations and warranties by the Company and such other terms and provisions as are customarily contained in underwriting agreements with respect to secondary distributions, which may include, without limitation, indemnities and contribution to the effect and to the extent provided in Article III and the provision of opinions of counsel and accountants’ letters as are customarily delivered by issuers to underwriters in secondary underwritten public offerings of securities. The Holders shall be a party to any such underwriting agreement and the representations and warranties by, and the other agreements on the part of, the Company to and for the benefit of such underwriters shall also be made to and for the benefit of such Holders of such securities, but only to the extent such representations and warranties and other agreements are customarily made by issuers to selling stockholders in secondary underwritten public offerings, and the Holders shall be required to make representations or warranties to, and other agreements with, the Company and the underwriters in

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connection with such underwriting agreement as are customarily made by selling stockholders in secondary underwritten public offerings; provided, however, that the Holders shall not be required to make any representations or warranties to the Company or the underwriters regarding such Holder’s knowledge about the Company or to undertake any indemnification obligations to the Company with respect thereto, except as otherwise provided in Article III), or to the underwriters with respect thereto, except to the extent of the indemnification being given to the Company and its controlling Persons in Article III.

(d) If (i) the managing underwriter for such Underwritten Offering advises the Company or (ii) the Company concludes, after consulting with its independent financial advisor (which shall be an investment banking firm of international standing), in either case, that in its opinion the number of Registrable Securities requested to be included in such Underwritten Offering exceeds the number of Registrable Securities that can be sold in an orderly manner in such offering within a price range acceptable to the Holders, the Company shall include in such Underwritten Offering the number of each Holder’s Registrable Securities which in the opinion of such managing underwriter or the Company’s independent financial advisor, as applicable, can be sold in an orderly manner within the price range of such offering.

(e) Unless the managing underwriter otherwise agrees, each Holder agrees not to effect any public sale or private offer or distribution of any shares of Company Common Stock or any other issue being registered or a similar security of the Company, or any securities convertible into or exchangeable or exercisable for such securities, during the fourteen (14) days prior to the anticipated effectiveness under the Securities Act of any underwritten registration of any such securities (or with respect to an underwritten takedown of any such securities under a shelf registration, prior to the pricing of such offer) and during such time period (not to exceed one hundred eighty (180) days) after the effectiveness under the Securities Act of any underwritten registration (or, with respect to an underwritten offering pursuant to a shelf registration statement, after the pricing of such offering) as the Company and the managing underwriter may agree (except as part of such underwritten registration or offering, as applicable).

2.2 Registration Procedures. If and whenever a Holder has requested that any Registrable Securities be registered pursuant to this Agreement under Article I, and subject to the limitations set forth in this Agreement, the Company will use its commercially reasonable efforts to effect the registration and the sale of such Registrable Securities in accordance with the intended method of disposition thereof, and pursuant thereto the Company will:

(a) if the Registration Statement is not automatically effective upon filing, use commercially reasonable efforts to cause such Registration Statement to become effective;

(b) notify such Holder, promptly after the Company receives notice thereof, of the time when such Registration Statement has been declared effective or a supplement to any Prospectus forming a part of such Registration Statement has been filed;

(c) after the Registration Statement becomes effective, notify such Holder of any request by the SEC that the Company amend or supplement such Registration Statement or Prospectus;

(d) prepare and file with the SEC such amendments and supplements to the Registration Statement and any Prospectus used in connection therewith as may be reasonably necessary to keep the Registration Statement effective and to comply with the provisions of the Securities Act with respect to the disposition of all Registrable Securities covered by the Registration Statement for the period required to effect the distribution of the Registrable Securities as set forth in Article I hereof;

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(e) to the extent necessary to properly sell any Registrable Securities, furnish to such Holder such numbers of copies of a Prospectus, including a preliminary Prospectus, as required by the Securities Act, and such other documents as such Holder may reasonably request in order to facilitate its disposition of its Registrable Securities;

(f) use its commercially reasonable efforts to register and qualify the Registrable Securities under such other securities or blue sky Laws of such jurisdictions as shall be reasonably requested by such Holder; provided, however, that the Company shall not be required in connection therewith or as a condition thereto to qualify to do business in or to file a general consent to service of process in any jurisdiction, unless the Company is already subject to service in such jurisdiction and except as may be required by the Securities Act, or subject itself to taxation in any such jurisdiction, unless the Company is already subject to taxation in such jurisdiction;

(g) use its commercially reasonable efforts to cause all such Registrable Securities to be listed on a national securities exchange or trading system and each securities exchange and trading system (if any) on which similar equity securities issued by the Company are then listed;

(h) provide a transfer agent and registrar for the Registrable Securities and provide a CUSIP number for all such Registrable Securities, in each case not later than the effective date of the Registration Statement;

(i) use its commercially reasonable efforts to furnish, on the date that shares of Registrable Securities are delivered to the underwriters for sale, if such securities are being sold through underwriters, (i) an opinion, dated as of such date, of the counsel representing the Company for the purposes of such registration, in form and substance as is customarily given to underwriters by the Company in an underwritten public offering, addressed to the underwriters and (ii) a letter dated as of such date, from the independent public accountants of the Company, in form and substance as is customarily given by independent public accountants to underwriters in an underwritten public offering, addressed to the underwriters;

(j) if requested by such Holder, cooperate with such Holder and the managing underwriter (if any) to facilitate the timely preparation and delivery of certificates (which shall not bear any restrictive legends unless required under applicable Law) representing securities sold under the Registration Statement, and enable such securities to be in such denominations and registered in such names as such Holder or the managing underwriter (if any) may request and keep available and make available to the Company’s transfer agent prior to the effectiveness of such Registration Statement a supply of such certificates;

(k) in the event of any underwritten public offering, enter into and perform its obligations under an underwriting agreement, in form and substance as is customarily given by the Company to underwriters in an underwritten public offering, with the underwriter(s) of such offering;

(l) upon execution of confidentiality agreements in form and substance satisfactory to the Company, promptly make available for inspection by such Holder, any underwriter(s) participating in any disposition pursuant to such Registration Statement, and any attorney or accountant or other agent retained by any such underwriter or selected by such Holder, all financial and other records, pertinent corporate documents, and properties of the Company (collectively, “Records”), and use commercially reasonable efforts to cause the Company’s officers, directors, employees, and independent accountants to supply all information reasonably requested by such Holder, an underwriter, attorney, accountant, or agent, in each case, as necessary or advisable to verify the accuracy of the information in such Registration Statement and to conduct appropriate due diligence in connection therewith; provided, Records that the

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Company determines, in good faith, to be confidential and that it notifies such Holder are confidential shall not be disclosed by such Holder unless the release of such Records is ordered pursuant to a subpoena or other order from a court of competent jurisdiction or is otherwise required by applicable Law. Such Holder agrees that information obtained by it as a result of such inspections shall be deemed confidential and shall not be used by it or its Affiliates (other than with respect to such Holder’s due diligence) unless and until such information is made generally available to the public, and further agrees that, upon learning that disclosure of such Records is sought in a court of competent jurisdiction, it shall give notice to the Company and allow the Company to undertake appropriate action to prevent disclosure of the Records deemed confidential;

(m) in the event of the issuance of any stop order suspending the effectiveness of such Registration Statement, or of any order suspending or preventing the use of any related Prospectus or suspending the qualification of any Registrable Securities included in such Registration Statement for sale in any jurisdiction, use its commercially reasonable efforts to obtain promptly the withdrawal of such order;

(n) promptly notify such Holder at any time when a Prospectus relating thereto is required to be delivered under the Securities Act of the happening of any event as a result of which the Prospectus included in the Registration Statement, as then in effect, includes an untrue statement of a material fact or omits to state any material fact required to be stated therein or necessary to make the statements therein not misleading in light of the circumstances under which they were made, and at the request of such Holder promptly prepare and furnish to such Holder a reasonable number of copies of a supplement to or an amendment of such Prospectus, or a revised Prospectus, as may be necessary so that, as thereafter delivered to the purchasers of such securities, such Prospectus shall not include an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading in light of the circumstances under which they were made (following receipt of any supplement or amendment to any Prospectus, such Holder shall deliver such amended, supplemental or revised Prospectus in connection with any offers or sales of Registrable Securities, and shall not deliver or use any Prospectus not so supplemented, amended or revised); and

(o) take all such other actions as are reasonably necessary in order to facilitate the disposition of such Registrable Securities.

2.3 Holder Obligations. Subject to Section 2.1(a), a Holder may not participate in any registration hereunder unless such Holder: (i) agrees to sell such Holder’s Registrable Securities on the basis provided in any underwriting arrangements approved by the Company; and (ii) completes and executes all questionnaires, powers of attorney, indemnities, underwriting agreements and other documents, each in customary form, reasonably required under the terms of such underwriting arrangements; provided, however, that such Holder shall not be required to make any representations or warranties in connection with any such registration other than representations and warranties as to (A) such Holder’s ownership of its Registrable Securities to be sold or transferred free and clear of all liens, claims and encumbrances; (B) such Holder’s power and authority to effect such transfer; and (C) such matters pertaining to compliance with securities Laws as may be reasonably requested; provided, further, that such liability will be limited, to the net amount received by such Holder from the sale of its Registrable Securities pursuant to such registration.

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2.4 Blackout Periods.

(a) (i) At any time when a Registration Statement effected pursuant to Article I relating to Registrable Securities is effective, upon written notice from the Company to a Holder that the board of directors of the Company (or any duly appointed committee thereof) has determined in good faith, with the advice of counsel, that such Holder’s sale of Registrable Securities pursuant to the Registration Statement would be reasonably likely to require disclosure of material non-public information the disclosure of which would not otherwise be required to be disclosed (provided that the Company shall not be required to disclose to such Holder any such material non-public information) and would be reasonably likely to have a material adverse effect on the Company or that such sale otherwise might not be in the best interests of the Company’s stockholders (an “Information Blackout”), such Holder shall suspend sales of Registrable Securities pursuant to such Registration Statement and (ii) if, while a Registration Request Notice or other registration request is pending pursuant to Article I, the board of directors of the Company (or any duly appointed committee thereof) determines that an Information Blackout is required, or that any such filing or the offering of any Registrable Securities would be reasonably likely to adversely affect or delay any proposed financing, offer or sale of securities, acquisition, disposition, corporate reorganization or other material transaction involving the Company, the Company shall deliver to such Holder a certificate to such effect signed by its Chief Executive Officer or Chief Financial Officer, and the Company shall not be required to file a Registration Statement, Prospectus or any amendment or any supplement thereto pursuant to Articles I (a “Registration Delay”); provided, that any such suspension or postponement under (i) and (ii) of this Section 2.4(a) shall only continue until the earliest of:

(1) the date upon which such material information is disclosed to the public or ceases to be material;

(2) ten (10) days after the Company’s delivery of such written notice to such Holder;

(3) in the case of clause (i) above, such time as the Company notifies such Holder that sales pursuant to such Registration Statement may be resumed; and

(4) in the case of clause (ii) above, the date upon which the financing, offer or sale of securities, acquisition, corporate reorganization or other material transaction referred to therein concludes or is abandoned.

The number of days from such suspension of sales by a Holder until the day when such sales may be resumed under clause (1), (2) or (3) hereof, or from the date of a notice of a Registration Delay until the date such affected registration process resumes under clause (1), (2) or (4) hereof, shall be called a “Blackout Period”. In no event may the Company deliver more than two (2) notices, collectively, of an Information Blackout and/or a Registration Delay in any twelve (12) consecutive month period, and the aggregate number of days in which any Blackout Periods may be in effect in any twelve (12) consecutive month period shall not exceed one hundred twenty (120) days.

(b) Any delivery by the Company of a written notice of a Registration Delay following a registration request by a Holder pursuant to Section 1.1, and before the effectiveness of the related Registration Statement, or of a written notice of an Information Blackout during the sixty (60) days immediately following effectiveness of any Registration Statement effected pursuant to Article I, shall give such Holder the right, by written notice to the Company within twenty (20) Business Days after the end of such Blackout Period, to cancel such registration and obtain one additional registration right during such calendar year under Article I.

(c) The Company shall not effect any public offering of its securities during any Blackout Period other than in connection with such proposed transaction described in Section 2.4(a).

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2.5 Transfer of Registration Rights. The registration rights of a Holder under this Agreement with respect to any Registrable Securities may be transferred or assigned to (i) an Affiliate of such Holder, or (ii) if the Holder is an Entity, a partner, stockholder or member thereof; provided, however, that (a) such Holder shall give the Company written notice prior to the time of such transfer stating the name and address of the transferee and identifying the securities with respect to which the rights under this Agreement are being transferred; (b) such transferee shall agree in writing, in form and substance satisfactory to the Company, to be bound as a Holder by the provisions of this Agreement; (c) such transferee is not a direct competitor of the Company; and (d) immediately following such transfer the further disposition of such securities by such transferee shall be restricted to the extent set forth under applicable Law.

2.6 Current Public Information. With a view to making available to each Holder the benefits of Rule 144 and Rule 144A promulgated under the Securities Act and other rules and regulations of the SEC that may at any time permit each Holder to sell securities of the Company to the public without registration, the Company covenants that it will (i) use its commercially reasonable efforts to file in a timely manner all reports and other documents required, if any, to be filed by it under the Securities Act and the Exchange Act and the rules and regulations adopted thereunder; and (ii) make available information necessary to comply with Rule 144 and Rule 144A, if available with respect to resales of the Registrable Securities under the Securities Act, at all times, all to the extent required from time to time to enable each Holder to sell Registrable Securities without registration under the Securities Act within the limitation of the exemptions provided by (x) Rule 144 and Rule 144A promulgated under the Securities Act (if available with respect to resales of the Registrable Securities), as such rules may be amended from time to time or (y) any other rules or regulations now existing or hereafter adopted by the SEC.

ARTICLE III—INDEMNIFICATION

3.1 Indemnification.

(a) The Company agrees to indemnify and reimburse, to the fullest extent permitted by Law, each Holder, with respect to the sale of Registrable Securities pursuant hereto, and each of its employees, advisors, agents, representatives, partners, officers, and directors and each Person who controls such Holder (within the meaning of the Securities Act or the Exchange Act) and any agent or investment advisor thereof (collectively, the “Seller Affiliates”): (i) against any and all losses, claims, damages, liabilities and expenses, joint or several (including, without limitation, attorneys’ fees and disbursements except as limited by Section 3.1(c)) based upon, arising out of, related to or resulting from any untrue or alleged untrue statement of a material fact contained in any Registration Statement or Prospectus or any amendment thereof or supplement thereto, or any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein not misleading; (ii) against any and all losses, liabilities, claims, damages and expenses whatsoever, as incurred, to the extent of the aggregate amount paid in settlement of any litigation or investigation or proceeding by any governmental agency or body, commenced or threatened, or of any claim whatsoever based upon, arising out of, related to or resulting from any such untrue statement or omission or alleged untrue statement or omission; and (iii) against any and all costs and expenses (including reasonable fees and disbursements of counsel) as may be reasonably incurred in investigating, preparing or defending against any litigation, investigation or proceeding by any governmental agency or body, commenced or threatened, or any claim whatsoever based upon, arising out of, related to or resulting from any such untrue statement or omission or alleged untrue statement or omission, or such violation of the Securities Act or Exchange Act, to the extent that any such expense or cost is not paid under subparagraph (i) or (ii) above; except insofar as any such statements are made in reliance upon information furnished to the Company by a Holder or any Seller Affiliate for use therein or arise from a Holder’s or any Seller Affiliate’s failure to deliver a copy of the Registration Statement or Prospectus or any amendments or supplements thereto after the Company has furnished such Holder or its Seller Affiliate with a sufficient number of copies of the same, in which case the Company will not so indemnify and reimburse such Holder or its Seller Affiliates. The reimbursements required by this Section 3.1(a) will be made by periodic payments during the course of the investigation or defense, as and when bills are received or expenses incurred.

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(b) In connection with any Registration Statement in which a Holder is participating as a seller of Registrable Securities, such Holder will furnish to the Company such information and affidavits as the Company reasonably requests for use in connection with any such Registration Statement or Prospectus and, to the fullest extent permitted by Law, such Holder will indemnify the Company and its directors and officers and each Person who controls the Company (within the meaning of the Securities Act or the Exchange Act) against any and all losses, claims, damages, liabilities and expenses (including, without limitation, reasonable attorneys’ fees and disbursements except as limited by Section 3.1(c)) resulting from any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement, Prospectus or any amendment thereof or supplement thereto or any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein not misleading, but only to the extent that such untrue statement or alleged untrue statement or omission or alleged omission is contained in any information or affidavit so furnished by such Holder or any of its Seller Affiliates specifically for inclusion in the Registration Statement; provided that such liability will be limited to the net amount received by such Holder from the sale of Registrable Securities pursuant to such Registration Statement; provided, however, that such Holder shall not be liable in any such case to the extent that prior to the filing of any such Registration Statement or Prospectus or amendment thereof or supplement thereto, such Holder has furnished to the Company information expressly for use in such Registration Statement or Prospectus or any amendment thereof or supplement thereto which corrected or made not misleading information previously furnished to the Company.

(c) Any Person entitled to indemnification hereunder will: (i) give prompt written notice to the indemnifying party of any claim with respect to which it seeks indemnification (provided that the failure to give such notice shall not limit the rights of such Person); and (ii) unless in such indemnified party’s reasonable judgment a conflict of interest between such indemnified and indemnifying parties may exist with respect to such claim, permit such indemnifying party to assume the defense of such claim with counsel reasonably satisfactory to the indemnified party; provided, however, that any person entitled to indemnification hereunder shall have the right to employ separate counsel and to participate in the defense of such claim, but the fees and expenses of such counsel shall be at the expense of such person unless (A) the indemnifying party has agreed to pay such fees or expenses or (B) the indemnifying party shall have failed to assume the defense of such claim and employ counsel reasonably satisfactory to such person. If such defense is not assumed by the indemnifying party as permitted hereunder, the indemnifying party will not be subject to any liability for any settlement made by the indemnified party without its consent (but such consent will not be unreasonably withheld, conditioned or delayed). If such defense is assumed by the indemnifying party pursuant to the provisions hereof, such indemnifying party shall not settle or otherwise compromise the applicable claim unless (i) such settlement or compromise contains a full and unconditional release of the indemnified party or (ii) the indemnified party otherwise consents in writing (which consent will not be unreasonably withheld, conditioned or delayed). An indemnifying party who is not entitled to, or elects not to, assume the defense of a claim will not be obligated to pay the fees and expenses of more than one counsel for all parties indemnified by such indemnifying party with respect to such claim, unless in the reasonable judgment of any indemnified party, a conflict of interest may exist between such indemnified party and any other of such indemnified parties with respect to such claim, in which event the indemnifying party shall be obligated to pay the reasonable fees and disbursements of such additional counsel or counsels.

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(d) Each party hereto agrees that, if for any reason the indemnification provisions contemplated by Section 3.1(a) or Section 3.1(b) are unavailable to or insufficient to hold harmless an indemnified party in respect of any losses, claims, damages, liabilities or expenses (or actions in respect thereof) referred to therein, then each indemnifying party shall contribute to the amount paid or payable by such indemnified party as a result of such losses, claims, liabilities or expenses (or actions in respect thereof) in such proportion as is appropriate to reflect the relative fault of the indemnifying party and the indemnified party in connection with the actions which resulted in the losses, claims, damages, liabilities or expenses as well as any other relevant equitable considerations. The relative fault of such indemnifying party and indemnified party shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or omission or alleged omission to state a material fact relates to information supplied by such indemnifying party or indemnified party, and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. The parties hereto agree that it would not be just and equitable if contribution pursuant to this Section 3.1(d) were determined by pro rata allocation (even if a Holder or any underwriters or all of them were treated as one entity for such purpose) or by any other method of allocation which does not take account of the equitable considerations referred to in this Section 3.1(d). The amount paid or payable by an indemnified party as a result of the losses, claims, damages, liabilities or expenses (or actions in respect thereof) referred to above shall be deemed to include any legal or other fees or expenses reasonably incurred by such indemnified party in connection with investigating or, except as provided in Section 3.1(c), defending any such action or claim. Notwithstanding the provisions of this Section 3.1(d), no Holder shall be required to contribute an amount greater than the dollar amount by which the net proceeds received by such Holder with respect to the sale of any Registrable Securities exceeds the amount of damages which such Holder has otherwise been required to pay by reason of any and all untrue or alleged untrue statements of material fact or omissions or alleged omissions of material fact made in any Registration Statement or Prospectus or any amendment thereof or supplement thereto related to such sale of Registrable Securities. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. Each Holder’s obligations in this Section 3.1(d) to contribute shall be several in proportion to the amount of Registrable Securities registered by them and not joint.

If indemnification is available under this Section 3.1, the indemnifying parties shall indemnify each indemnified party to the full extent provided in Section 3.1(a) and Section 3.1(b) without regard to the relative fault of said indemnifying party or indemnified party or any other equitable consideration provided for in this Section 3.1(d) subject, in the case of a Holder, to the limited dollar amounts set forth in Section 3.1(b).

(e) The indemnification and contribution provided for under this Agreement will remain in full force and effect regardless of any investigation made by or on behalf of the indemnified party or any officer, director or controlling Person of such indemnified party and will survive the transfer of securities.

ARTICLE IV—TERMINATION

4.1 Termination. The provisions of this Agreement shall terminate and be of no further force and effect upon the earlier of (a) the four (4) year anniversary following the Closing and (b) the date when all Registrable Securities have been sold or are available to be sold under Rule 144 promulgated under the Securities Act without regard to volume limits.

ARTICLE V—MISCELLANEOUS

5.1 Amendment. Any provision of this Agreement may be amended or waived if, but only if, such amendment or waiver is in writing and is signed, in the case of an amendment, by each party to this Agreement or in the case of a waiver, by the party against whom the waiver is to be effective.

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5.2 Counterparts and Facsimile. This Agreement may be signed in any number of counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument. Signatures to this Agreement transmitted by facsimile transmission, by electronic mail in PDF form, or by any other electronic means designed to preserve the original graphic and pictorial appearance of a document, will be deemed to have the same effect as physical delivery of the paper document bearing the original signatures. This Agreement shall become effective when each party hereto shall have received counterparts hereof signed by all of the other parties hereto. Until and unless each party has received a counterpart hereof signed by the other party hereto, this Agreement shall have no effect and no party shall have any right or obligation hereunder (whether by virtue of any other oral or written agreement or other communication).

5.3 Governing Law; Submission to Jurisdiction; Waiver of Jury Trial.

(a) This Agreement shall be governed by and construed in accordance with and governed by the Laws of the State of Delaware, without regard to the conflicts of law rules of such State that would result in the application of any Law other than the Law of the State of Delaware.

(b) Each party to this Agreement hereby irrevocably and unconditionally (i) consents to the submission to the exclusive jurisdiction of the Court of Chancery of the State of Delaware sitting in Wilmington, Delaware for any proceedings arising out of or relating to this Agreement or the transactions contemplated hereby, (ii) agrees not to commence any proceeding relating thereto except in such court and in accordance with the provisions of this Agreement, (iii) agrees that service of any process, summons, notice or document by U.S. registered mail, or otherwise in the manner provided for notices in Section 3.5 hereof, shall be effective service of process for any such proceeding brought against it in any such court, (iv) waives, to the fullest extent it may legally and effectively do so, any objection which it may now or hereafter have to the laying of venue of any such proceeding in such courts and (v) agrees not to plead or claim in any court that any such proceeding brought in any such court has been brought in an inconvenient forum. Each of the parties hereto agrees that a final judgment in any such proceeding shall be conclusive and may be enforced in other jurisdictions by suit on the judgment or in any other manner provided by applicable Law. Nothing in this Agreement will affect the right of any party to this Agreement to serve process in any other manner permitted by applicable Law.

(c) THE PARTIES HERETO WAIVE, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY RIGHT TO A TRIAL BY JURY IN ANY ACTION OR PROCEEDING (WHETHER BASED ON CONTRACT, EQUITY, TORT OR ANY OTHER THEORY) DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS AGREEMENT, THE TRANSACTION AGREEMENT, OR THE NEGOTIATION, EXECUTION, PERFORMANCE, OR ENFORCEMENT OF THIS AGREEMENT, THE TRANSACTION AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THEREBY, REGARDLESS OF WHICH PARTY INITIATES SUCH ACTION OR PROCEEDING. EACH PARTY (A) CERTIFIES THAT NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER AND (B) ACKNOWLEDGES THAT IT AND THE OTHER PARTIES HERETO HAVE BEEN INDUCED TO ENTER INTO THIS AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION.

5.4 Notices. All notices and other communications required or permitted to be given hereunder shall be in writing and shall be deemed given if delivered personally, transmitted by facsimile or e-mail (and confirmed), mailed by registered or certified mail with postage prepaid and return receipt requested, or sent by commercial overnight courier, courier fees prepaid (if available; otherwise, by the next best class of service available), to the parties at the following addresses:

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If to the Company:

Approach Resources Inc.

6500 West Freeway, Suite 800

Fort Worth, Texas 76116

Attention: J. Curtis Henderson

Facsimile: (817) 989-9001

With copies to (which shall not constitute notice):

Weil, Gotshal & Manges LLP

200 Crescent Court, Suite 300

Dallas, Texas 75201

Attention: Rodney Moore

Facsimile: (214) 746-8102

Email: rodney.moore@weil.com

If to any Holder, at its address listed on the signature pages hereof.

Any party may from time to time change its address or designee for notification purposes by giving the other parties prior notice in the manner specified above of the new address or the new designee and the subsequent date upon which the change shall be effective.

5.5 Entire Agreement; Etc.. This Agreement (including the Exhibit hereto) constitutes the entire agreement among the parties hereto with respect to the subject matter hereof and supersedes all other prior agreements and understandings, both written and oral, among the parties hereto with respect to the subject matter hereof.

5.6 Headings. The Article and Section headings in this Agreement are for convenience of reference only, do not constitute a part of this Agreement and shall not limit, extend or otherwise affect the meaning or interpretation of the terms and provisions of this Agreement.

5.7 Severability. If any term, provision, covenant or restriction of this Agreement is held by a court of competent jurisdiction or other Governmental Entity to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated so long as the economic or legal substance of the transactions contemplated hereby is not affected in any manner materially adverse to any party hereto. Upon such a determination, the parties hereto shall negotiate in good faith to modify this Agreement so as to effect the original intent of the parties hereto as closely as possible in an acceptable manner in order that the transactions contemplated hereby be consummated as originally contemplated to the fullest extent possible.

5.8 No Third Party Beneficiaries. Subject to the following sentence, nothing in this Agreement is intended or shall be construed to give any Person, other than the parties hereto and their respective successors, assigns and legal representatives, any legal or equitable right, remedy or claim under or in respect of this Agreement or any provision contained herein.

5.9 Expenses. Except as otherwise explicitly contemplated by this Agreement, each party will bear and pay the costs and expenses incurred by such party in connection with the transactions contemplated under this Agreement.

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5.10 Existing Registration Rights Agreement. Notwithstanding anything to the contrary in this Agreement, the provisions of this Agreement are subject to the Existing Registration Right Agreement. To the extent a Holder has any right, or the Company has any obligation, that is in conflict with or affected by the Existing Registration Rights Agreement, the provisions of the Existing Registration Rights Agreement shall govern and the provisions hereof shall be read in conjunction with, and subject to, such provisions in the Existing Registration Rights Agreement.

5.11 Other Definitional and Interpretive Matters. Unless otherwise expressly provided or the context otherwise requires, for purposes of this Agreement the following rules of interpretation apply.

(a) When calculating the period of time before which, within which or following which any act is to be done or step taken pursuant to this Agreement, the date that is the reference date in calculating such period is excluded. If the last day of such period is a non-Business Day, the period in question ends on the next succeeding Business Day.

(b) Any reference in this Agreement to $ means U.S. dollars.

(c) The Exhibit to this Agreement are hereby incorporated and made a part hereof as if set forth in full in this Agreement and are an integral part of this Agreement. Any capitalized terms used in any Exhibit but not otherwise defined therein are defined as set forth in this Agreement.

(d) Any reference in this Agreement to gender includes all genders, and words imparting the singular number also include the plural and vice versa.

(e) The division of this Agreement into Articles, Sections and other subdivisions and the insertion of headings are for convenience of reference only and do not affect, and should not be utilized in, the construction or interpretation of this Agreement.

(f) All references in this Agreement to any “Article,” “Section or “Exhibit” are to the corresponding Article, Section or Exhibit of this Agreement.

(g) The words “herein,” “hereinafter,” “hereof,” and “hereunder” refer to this Agreement as a whole and not merely to a subdivision in which such words appear unless the context otherwise requires.

(h) The word “including” or any variation thereof means “including, but not limited to,” and does not limit any general statement that it follows to the specific or similar items or matters immediately following it.

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Exhibit A

Certain Definitions

Agreement. “Agreement” has the meaning set forth in the Introductory Paragraph.

Affiliate. “Affiliate” means, with respect to any Person, any Person who, directly or indirectly through one or more intermediaries, controls, is controlled by or is under common control with any Person.

Beneficial Ownership. “Beneficial Ownership” and terms of similar import shall be as defined under and determined pursuant to Rule 13d-3 promulgated under the Exchange Act.

Blackout Period. “Blackout Period” has the meaning set forth in Section 2.4(a).

Business Day. “Business Day” means any day other than (i) a Saturday, Sunday or a federal holiday, or (ii) a day on which commercial banks in New York City, New York or Fort Worth, Texas are authorized or required to be closed.

Closing. “Closing” has the meaning given to such term in the Exchange Agreement.

Company. “Company” has the meaning set forth in the Introductory Paragraph.

Company Common Stock. “Company Common Stock” has the meaning set forth in the Recitals.

Entity. “Entity” means any corporation (including any non-profit corporation), general partnership, limited partnership, limited liability partnership, joint venture, estate, trust, cooperative, foundation, society, political party, union, company (including any limited liability company or joint stock company), firm or other enterprise, association, organization or entity.

Effectiveness Period. “Effectiveness Period” has the meaning set forth in Section 1.1(a).

Exchange Act. “Exchange Act” means the Securities Exchange Act of 1934, as amended, or any similar federal statute, and the rules and regulations promulgated by the SEC thereunder.

Exchange Agreement. “Exchange Agreement” has the meaning set forth in the Recitals.

Excluded Registration. “Excluded Registration” means a registration under the Securities Act of (i) securities registered on Form S-8 or any similar successor form and (ii) securities registered to effect the acquisition of or combination with another Person.

Existing Registration Rights Agreement. “Existing Registration Rights Agreement” means the Registration Rights Agreement, dated as of November 14, 2007, by and among the Company and each of the other parties thereto.

Governmental Entity. “Governmental Entity” means any U.S., foreign, federal, national, state or local government or political subdivision thereof, any entity, agency, authority or body exercising executive, legislative, judicial, regulatory or administrative functions of or pertaining to government, any court, tribunal or arbitrator, and any self-regulatory organization.

Holder. “Holder” has the meaning set forth in the Introductory Paragraph.

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Information Blackout. “Information Blackout” has the meaning set forth in Section 2.4(a).

Law. “Law” means any federal, state, local, municipal, foreign or other law, statute, legislation, constitution, principle of common law, resolution, ordinance, code, edict, decree, proclamation, treaty, convention, rule, regulation, ruling, directive, pronouncement, requirement, specification, determination, decision, opinion or interpretation issued, enacted, adopted, passed, approved, promulgated, made, implemented or otherwise put into effect by or under the authority of any Governmental Entity (including those laws relating to record keeping, customs, export and sanctions compliance, foreign assets control, foreign corrupt practices, possession and handling of classified information or zoning).

Material Adverse Effect. “Material Adverse Effect” has the meaning set forth in Section 1.2(b).

Participating Holder. “Participating Holder” has the meaning set forth in Section 1.2(a).

Person. “Person” means any individual, Entity or Governmental Entity.

Prospectus. “Prospectus” means the prospectus (including any preliminary, final or summary prospectus) included in any Registration Statement, all amendments and supplements to such prospectus and all other material incorporated by reference in such prospectus.

Records. “Records” has the meaning set forth in Section 2.2(l).

Register. “Register,” “registered” and “registration” refer to a registration effected by preparing and filing a Registration Statement in compliance with the Securities Act, and the declaration or ordering of the effectiveness of such Registration Statement.

Registrable Securities. “Registrable Securities” means, at any time, the Company Common Stock owned by a Holder, whether owned on the date hereof or acquired hereafter; provided, however, that Registrable Securities shall not include any shares (i) the sale of which has been registered pursuant to the Securities Act and which shares have been sold pursuant to such registration; (ii) which have been sold on any U.S. national securities exchange or quotation system on which the Registrable Securities are then listed or traded, pursuant to Rule 144 under the Securities Act or otherwise; (iii) that have been sold, transferred or disposed of by a Holder to a Person that is not an Affiliate of such Holder, and such Person may immediately thereafter fully transfer such Registrable Securities without restriction under the applicable securities laws of the United States; or (iv) which have been sold pursuant to Rule 144 under the Securities Act or are eligible for resale pursuant to Rule 144 under the Securities Act without regard to volume or manner of sale restrictions.

Registration Delay. “Registration Delay” has the meaning set forth in Section 2.4(a).

Registration Expenses. “Registration Expenses” means all expenses (other than underwriting discounts and commissions) arising from or incident to the registration of Registrable Securities in compliance with this Agreement, including, without limitation: (i) SEC, stock exchange, FINRA and other registration and filing fees; (ii) all fees and expenses incurred in connection with complying with any securities or blue sky Laws (including, without limitation, fees, charges and disbursements of counsel in connection with blue sky qualifications of the Registrable Securities); (iii) all printing, messenger and delivery expenses; (iv) the fees, charges and disbursements of counsel to the Company and of its independent public accountants and any other accounting and legal fees, charges and expenses incurred by the Company (including, without limitation, any expenses arising from any special audits or “comfort” letters required in connection with or incident to any registration); (v) the fees and expenses incurred in connection with the listing of the Registrable Securities on any national securities exchange or the quotation of Registrable Securities on any

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inter-dealer quotation system; (vi) the fees and expenses incurred by the Company in connection with any “road show” for underwritten offerings; and (vii) reasonable fees, charges and disbursements of counsel to the Holders, including, for the avoidance of doubt, any expenses of counsel to the Holders in connection with the filing or amendment of any Registration Statement or Prospectus hereunder; provided that Registration Expenses shall only include the fees and expenses of one counsel to the Holders (and one local counsel per jurisdiction) with respect to any offering.

Registration Request Notice. “Registration Request Notice” has the meaning set forth in Section 1.1(a).

Registration Statement. “Registration Statement” means any registration statement of the Company that covers the resale of any Registrable Securities pursuant to the provisions of this Agreement filed with, or to be filed with, the SEC under the rules and regulations promulgated under the Securities Act, including the related Prospectus, amendments and supplements to such registration statement, including pre- and post-effective amendments, and all exhibits, financial information and all other material incorporated by reference in such registration statement.

SEC. “SEC” means the Securities and Exchange Commission or any other Federal agency at the time administering the Securities Act.

Securities Act. “Securities Act” means the Securities Act of 1933, as amended, or any similar Federal statute, and the rules and regulations promulgated by the SEC thereunder.

Seller Affiliates. “Seller Affiliates” has the meaning set forth in Section 3.1.

Trading Forum. “Trading Forum” has the meaning set forth in Section 1.4.

Underwriting Request. “Underwriting Request” has the meaning set forth in Section 2.1(a).

Underwritten Offering. ‘Underwritten Offering” has the meaning set forth in Section 2.1(a).

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed by their respective authorized officers as of the date first written above.

[Signature page to Registration Rights Agreement]

[Signature page to Registration Rights Agreement]

[Signature page to Registration Rights Agreement]