Exhibit 4.1

FORM OF STOCKHOLDER’S AGREEMENT

This STOCKHOLDER’S AGREEMENT (this “Agreement”), dated as of             , 2016, is entered into by and among RSP Permian, Inc., a Delaware corporation (the “Company”), and Kayne Anderson Capital Advisors, LP, a California limited partnership (“Kayne Anderson”).

RECITALS

WHEREAS, the Company is a party to (i) that certain Membership Interest Purchase and Sale Agreement by and among Silver Hill Energy Partners Holdings, LLC, a Delaware limited liability company (“SHEP I Partners”), Silver Hill Energy Partners, LLC, a Delaware limited liability company (“SHEP I”), RSP Permian, L.L.C., a Delaware limited liability company (“RSP LLC”), and the Company dated as of October 11, 2016 (the “SHEP I MIPSA”) and (ii) that certain Membership Interest Purchase and Sale Agreement by and among Silver Hill Energy Partners II, LLC, a Delaware limited liability company (“SHEP II Partners”), Silver Hill E&P II, LLC, a Delaware limited liability company (“SHEP II”), RSP LLC and the Company dated as of October 11, 2016 (the “SHEP II MIPSA”); and

WHEREAS, this Agreement is being entered into in connection with the consummation of the transactions contemplated by the SHEP I MIPSA to set forth certain understandings among the Company and Kayne Anderson with respect to certain corporate governance matters.

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

ARTICLE I

DEFINITIONS

Section 1.1 Certain Definitions. As used in this Agreement, the following terms shall have the following meanings:

“Affiliate” of a specified Person is a Person that directly, or indirectly through one or more intermediaries, controls, is controlled by, or is under common control with, the Person specified.

“Agreement” has the meaning set forth in the preamble to this Agreement.

“Beneficial Owner” of a security is a Person who directly or indirectly, through any contract, arrangement, understanding, relationship or otherwise has or shares voting power, which includes the power to vote, or to direct the voting of, such security and/or investment power, which includes the power to dispose, or to direct the disposition of, such security. The terms “Beneficially Own” and “Beneficial Ownership” shall have correlative meanings.

“Board” means the Board of Directors of the Company.

“Closing” has the meaning set forth in the SHEP II MIPSA.

“Common Stock” means the common stock, par value $0.01 per share, of the Company.

“Company” has the meaning set forth in the preamble to this Agreement.

“Equity Securities” means any equity securities of the Company or any options, warrants or other securities that are directly or indirectly convertible into, or exercisable or exchangeable for, any equity securities of the Company.

“Kayne Anderson” has the meaning set forth in the preamble to this Agreement.

“Kayne Entities” has the meaning set forth in Section 2.1(a) of this Agreement.

“Person” means any individual, corporation, firm, partnership, joint venture, limited liability company, estate, trust, business association, organization, any court, administrative agency, regulatory body, commission or other governmental authority, board, bureau or instrumentality, domestic or foreign and any subdivision thereof or other entity, and also includes any managed investment account.

“Proceeding” has the meaning set forth in Section 4.7 of this Agreement.

“RSP LLC” has the meaning set forth in the recitals of this Agreement

“Selected Courts” has the meaning set forth in Section 4.7 of this Agreement.

“SHEP I” has the meaning set forth in the recitals of this Agreement.

“SHEP I MIPSA” has the meaning set forth in the recitals of this Agreement.

“SHEP I Partners” has the meaning set forth in the recitals of this Agreement.

“SHEP II” has the meaning set forth in the recitals of this Agreement.

“SHEP II MIPSA” has the meaning set forth in the recitals of this Agreement.

“SHEP II Partners” has the meaning set forth in the recitals of this Agreement.

Section 1.2 Rules of Construction. Unless the context otherwise requires:

(a) References in the singular or to “his,” “her,” “it,” “itself” or other like references, and references in the plural or the feminine or masculine reference, as the case may be, shall also, when the context so requires, be deemed to include the plural or singular, or the masculine or feminine reference, as the case may be;

(b) References to Articles and Sections shall refer to articles and sections of this Agreement, unless otherwise specified;

(c) The headings in this Agreement are for convenience and identification only and are not intended to describe, interpret, define or limit the scope, extent or intent of this Agreement or any provision thereof;

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(d) This Agreement shall be construed without regard to any presumption or other rule requiring construction against the party that drafted and caused this Agreement to be drafted; and

(e) References to “including” in this Agreement shall mean “including, without limitation,” whether or not so specified.

ARTICLE II

STANDSTILL AND GOVERNANCE MATTERS

Section 2.1 Standstill. During the period commencing on the date hereof and ending on the termination of this Agreement pursuant to Section 3.1, without the prior written consent of the Board, Kayne Anderson shall not, and shall cause the investment funds controlled by Kayne Anderson (together with Kayne Anderson, the “Kayne Entities”) not to, directly or indirectly:

(a) acquire Beneficial Ownership of additional shares of Common Stock such that, upon the consummation of such acquisition, the Kayne Entities would own in the aggregate more than 29.9% of the Common Stock, whether directly or indirectly;

(b) engage in a hostile takeover of the Company (including by means of a tender offer or soliciting proxies or written consents, other than as recommended by the Board), whether by merger, consolidation, recapitalization, business combination, partnership, joint venture, acquisition or similar transaction involving the Company;

(c) form, join or participate in a “group” (within the meaning of Section 13(d) of the Exchange Act) with respect to any voting securities of the Company in respect of any action otherwise prohibited pursuant to this Section 2.1; or

(d) “solicit” any “proxies” (as such terms are used in the proxy rules and regulations of the Securities and Exchange Commission) or consents in favor of any action prohibited by this Section 2.1; or

(e) enter into agreements with any third party to do any of the foregoing.

Section 2.2 Limitations. Notwithstanding the foregoing, nothing in this Agreement shall in any way limit the right of the Kayne Entities or their respective Affiliates to (and it shall not be deemed a breach of this Agreement for them to):

(a) privately communicate with, including making any offer or proposal to, the Board;

(b) vote their shares of Common Stock at any meeting of the stockholders of the Company or otherwise exercise their rights as stockholders; or

(c) sell, transfer, distribute, hedge or otherwise dispose of any of their shares of Common Stock.

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ARTICLE III

TERMINATION

Section 3.1 Termination. This Agreement shall terminate and Section 2.1 shall automatically be inoperative and of no force or effect upon the earlier to occur of (a) any Person or group shall have acquired or entered into a definitive agreement to acquire more than 50% of the equity securities of the Company or assets of the Company representing more than 50% of the consolidated earning power of the Company, whether by merger, tender offer or otherwise (including any merger or similar transaction involving the Company in which the shareholders of any third party own, directly or indirectly, 50% or more of the combined company), (b) a third party makes a tender offer for more than 50% of the equity securities of Company, (c) the Company or any of its subsidiaries makes an assignment for the benefit of creditors or commences any proceeding under any bankruptcy, reorganization, insolvency, dissolution or liquidation law of any jurisdiction, (d) any such petition is filed or any such proceeding is commenced against the Company or any of its subsidiaries and either (i) the Company or such subsidiary by any act indicates its approval thereof, consent thereto or acquiescence therein or (ii) such petition, application or proceeding is not dismissed within thirty (30) days, (e) the date of the second anniversary this Agreement or (f) the date on which the Kayne Entities Beneficially Own in the aggregate less than 10% of the outstanding shares of Common Stock.

ARTICLE IV

MISCELLANEOUS

Section 4.1 Notices. All notices, requests, consents and other communications hereunder to any party shall be in writing and shall be personally delivered, sent by nationally recognized overnight courier or mailed by registered or certified mail to such party at the address set forth below (or such other address as shall be specified by like notice). Notices will be deemed to have been given hereunder when personally delivered, one calendar day after deposit with a nationally recognized overnight courier and five calendar days after deposit in U.S. mail.

RSP Permian, Inc.

3141 Hood Street, Suite 701

Dallas, Texas 75219

Attention: Jim Mutrie

with a copy to:

Vinson & Elkins LLP

1001 Fannin Street

Suite 2500, Houston, TX 77002

Attn: Stephen M. Grill

E-mail: sgill@velaw.com

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Kayne Anderson Capital Advisors, LP

Floor 14, 811 Main Street

Houston, Texas 77002

Attention: Kevin Brophy

with a copy to:

DLA Piper LLP (US)

1000 Louisiana Street, Suite 2800

Houston, Texas 77002-5005

Attn: Jack Langlois

Phone: 713-425-8419

Fax: 713-300-6019

Email: jack.langlois@dlapiper.com

Section 4.2 Severability. The provisions of this Agreement shall be deemed severable, and the invalidity or unenforceability of any provision shall not affect the validity or enforceability of the other provisions hereof. If any provision of this Agreement, or the application thereof to any Person or any circumstance, is found to be invalid or unenforceable in any jurisdiction, a suitable and equitable provision shall be substituted therefor in order to carry out, so far as may be valid and enforceable, the intent and purpose of such invalid or unenforceable provision and the remainder of this Agreement and the application of such provision to other Persons or circumstances shall not be affected by such invalidity or unenforceability, nor shall such invalidity or unenforceability affect the validity or enforceability of such provision, or the application thereof, in any other jurisdiction.

Section 4.3 Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed an original and all of which, taken together, shall be considered one and the same agreement.

Section 4.4 Entire Agreement; No Third Party Beneficiaries. This Agreement constitutes the entire agreement and supersedes all other prior agreements, both written and oral, among the parties with respect to the subject matter hereof and is not intended to confer upon any Person, other than the parties hereto, any rights or remedies hereunder.

Section 4.5 Further Assurances. Each party shall execute, deliver, acknowledge and file such other documents and take such further actions as may be reasonably requested from time to time by the other parties hereto to give effect to and carry out the transactions contemplated herein.

Section 4.6 Governing Law; Equitable Remedies. THIS AGREEMENT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF DELAWARE (WITHOUT GIVING EFFECT TO CONFLICT OF LAWS PRINCIPLES THEREOF). The parties hereto agree that irreparable damage would occur in the event that any of the provisions of this Agreement were not performed in accordance with its specific terms or was otherwise breached. It is accordingly agreed that the parties hereto shall be entitled to seek an injunction or injunctions and other equitable remedies to prevent breaches of this Agreement and to seek to enforce specifically the terms and provisions hereof in any of the

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Selected Courts (as defined below), this being in addition to any other remedy to which they are entitled to seek at law or in equity. Any requirements for the securing or posting of any bond with respect to such remedy are hereby waived by each of the parties hereto.

Section 4.7 Consent To Jurisdiction. With respect to any suit, action or proceeding (“Proceeding”) arising out of or relating to this Agreement, each of the parties hereto hereby irrevocably submits to the exclusive jurisdiction of the Court of Chancery of the State of Delaware and the United States District Court for the District of Delaware and the appellate courts therefrom (the “Selected Courts”) and waives any objection to venue being laid in the Selected Courts whether based on the grounds of forum non conveniens or otherwise and hereby agrees not to commence any such Proceeding other than before one of the Selected Courts; provided, however, that a party may commence any Proceeding in a court other than a Selected Court solely for the purpose of enforcing an order or judgment issued by one of the Selected Courts; consents to service of process in any Proceeding by the mailing of copies thereof by registered or certified mail, postage prepaid, or by recognized international express carrier or delivery service, to the Company or Kayne Anderson at their respective addresses referred to in Section 4.1 hereof; provided, however, that nothing herein shall affect the right of any party hereto to serve process in any other manner permitted by law; and TO THE EXTENT NOT PROHIBITED BY APPLICABLE LAW THAT CANNOT BE WAIVED, WAIVES, AND COVENANTS THAT IT WILL NOT ASSERT (WHETHER AS PLAINTIFF, DEFENDANT OR OTHERWISE) ANY RIGHT TO TRIAL BY JURY IN ANY ACTION ARISING IN WHOLE OR IN PART UNDER OR IN CONNECTION WITH THIS AGREEMENT, WHETHER NOW EXISTING OR HEREAFTER ARISING, AND WHETHER SOUNDING IN CONTRACT, TORT OR OTHERWISE, AND AGREES THAT ANY OF THEM MAY FILE A COPY OF THIS PARAGRAPH WITH ANY COURT AS WRITTEN EVIDENCE OF THE KNOWING, VOLUNTARY AND BARGAINED-FOR AGREEMENT AMONG THE PARTIES IRREVOCABLY TO WAIVE THE RIGHT TO TRIAL BY JURY IN ANY PROCEEDING WHATSOEVER BETWEEN THEM RELATING TO THIS AGREEMENT AND TO HAVE ALL MATTERS RELATING TO THIS AGREEMENT BE TRIED IN A COURT OF COMPETENT JURISDICTION BY A JUDGE SITTING WITHOUT A JURY.

Section 4.8 Amendments; Waivers.

(a) No provision of this Agreement may be amended or waived unless such amendment or waiver is in writing and signed, in the case of an amendment, by each of the parties hereto, or in the case of a waiver, by each of the parties against whom the waiver is to be effective.

(b) No failure or delay by any party in exercising any right, power or privilege hereunder shall operate as waiver thereof nor shall any single or partial exercise thereof preclude any other or further exercise thereof or the exercise of any other right, power or privilege. The rights and remedies herein provided shall be cumulative and not exclusive of any rights or remedies provided by law.

Section 4.9 Assignment. Neither this Agreement nor any of the rights or obligations hereunder shall be assigned by any of the parties hereto without the prior written consent of the other parties. Subject to the preceding sentence, this Agreement will be binding upon, inure to

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the benefit of and be enforceable by the parties and their respective successors and assigns; provided however, that this Agreement shall not be binding upon or enforceable against (i) any un-Affiliated buyer, transferee, distributee or other successor-in-interest of Common Stock held by any Kayne Entity or (ii) any limited partner of a Kayne Entity.

SIGNATURE PAGE FOLLOWS.

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IN WITNESS WHEREOF, the parties have caused this Agreement to be duly executed and delivered, all as of the date first set forth above.

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