Exhibit 5.1

September 20, 2012

Approach Resources Inc.

One Ridgmar Center

6500 West Freeway, Suite 800

Fort Worth, Texas 76116

Ladies and Gentlemen:

We have acted as special counsel to Approach Resources Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of (i) the registration statement on Form S-3 (File No. 333-174318) (the “Registration Statement”) which was initially filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), and the rules and regulations promulgated thereunder, on May 18, 2011 and (ii) the prospectus supplement dated September 19, 2012 (the “Prospectus Supplement”) and filed with the Commission on September 20, 2012, under Rule 424(b)(5) as promulgated under the Securities Act, relating to the sale by the Company of 5,000,000 shares of the Company’s common stock, par value $0.01 per share (“Common Stock”), to be sold in an underwritten public offering pursuant to that certain Underwriting Agreement dated September 19, 2012 (the “Underwriting Agreement”) between the Company and J.P. Morgan Securities LLC, as representative of the underwriters named therein, and relating to the sale by the Company of up to an additional 750,000 shares of Common Stock, which may be sold upon exercise by the underwriters of their option to purchase additional shares of Common Stock granted by the Company in the Underwriting Agreement. As used herein, “Securities” means the shares of Common Stock that may be sold under the Underwriting Agreement, including shares sold pursuant to any exercise of the underwriters of their option to purchase additional shares.

In connection with this opinion letter, we have examined original counterparts or copies of original counterparts of the Registration Statement, the Prospectus Supplement, and the Underwriting Agreement. We have also examined originals or copies of such other records of the Company, certificates of public officials and of officers or other representatives of the Company and agreements and other documents as we have deemed necessary, subject to the assumptions set forth below, as a basis for the opinions expressed below.

In rendering the opinions expressed below, we have assumed:

(i) The genuineness of all signatures.

(ii) The authenticity of the originals of the documents submitted to us.

(iii) The conformity to authentic originals of any documents submitted to us as copies.

Approach Resources, Inc.

September 20, 2012

Page 2

(iv) As to matters of fact, the truthfulness of the representations made or otherwise incorporated in the Underwriting Agreement and representations and statements made in certificates of public officials and officers or other representatives of the Company.

Based upon the foregoing, and subject to the qualifications and limitations herein set forth, we are of the opinion that the Securities have been duly authorized by all necessary corporate action on the part of the Company and, when sold as described in the Prospectus Supplement, will be validly issued, fully paid and nonassessable.

Our opinion is limited to Delaware General Corporation Law, including all applicable provisions of the constitution of each such jurisdiction and reported judicial decisions interpreting such laws, and we do not express any opinion herein concerning any other laws.

This opinion letter has been prepared, and is to be understood, in accordance with customary practice of lawyers who regularly give and lawyers who regularly advise recipients regarding opinions of this kind, is limited to the matters expressly stated herein and is provided solely for purposes of complying with the requirements of the Underwriting Agreement, and no opinions may be inferred or implied beyond the matters expressly stated herein. The opinions expressed herein are rendered and speak only as of the date hereof and we specifically disclaim any responsibility to update such opinions subsequent to the date hereof or to advise you of subsequent developments affecting such opinions.

We consent to the reference to this firm in the Prospectus Supplement under the caption “Legal Matters” as the attorneys who will pass upon the legal validity of the Securities and to the filing of this opinion as Exhibit 5.1 to a Current Report on Form 8-K. Our consent, however, shall not constitute an admission to our being experts as provided for in Sections 7 and 11 of the Securities Act.

WPW/JWH/JEB

RHS