SECOND AMENDMENT TO THE APPROACH RESOURCES INC. 2007 STOCK INCENTIVE PLAN

Exhibit 10.1

SECOND AMENDMENT TO THE

APPROACH RESOURCES INC.

2007 STOCK INCENTIVE PLAN

This Second Amendment (the “Second Amendment”) to the Approach Resources Inc. 2007 Stock Incentive Plan, as amended from time to time (the “Plan”), is made effective as of May 31, 2012 (the “Amendment Effective Date”), by Approach Resources Inc., a Delaware corporation (“Approach”), subject to approval by Approach’s stockholders.

W I T N E S S E T H:

WHEREAS, Approach established the Plan, originally effective as of June 28, 2007, under which Approach is authorized to grant equity-based incentive awards to certain employees and service providers of Approach and its subsidiaries;

WHEREAS, Section 14.1 of the Plan provides that Approach’s board of directors (the “Board”) may amend the Plan subject to, in certain circumstances, the approval of the holders of at least a majority of Approach’s shares of common stock;

WHEREAS, the Board now desires to amend the Plan in the manner contemplated hereby, subject to approval by Approach’s shareholders at the Company’s 2012 annual meeting, to (a) delete the Plan’s “evergreen” provision in Section 4.1(a), (b) provide for a maximum number of shares available for grant of Awards under the Plan after the Amendment Effective Date at 2,100,000, (c) extend the term of the Plan until May 30, 2022, and (d) remove the Plan provisions permitting (i) shares tendered by an option holder to pay for the exercise of an option and (ii) shares withheld for taxes, in either case, to be recycled back into the Plan for future Awards; and

WHEREAS, capitalized terms used but not defined herein shall have the same meaning as set forth in the Plan.

NOW, THEREFORE, the Plan shall be amended as of the Amendment Effective Date as set forth below:

1. Section 1.3 of the Plan is hereby deleted and replaced in its entirety with the following:

1.3 Effectiveness and Term. This Plan was originally effective on June 28, 2007 (the “Effective Date”), the date of its approval by the holders of at least a majority of the shares of Common Stock. The Plan was subsequently amended by the Board effective December 31, 2008. The Plan was subsequently amended by the Board and approved by Approach’s shareholders effective May 31, 2012. Unless terminated earlier by the Board pursuant to Section 14.1, this Plan shall terminate on May 30, 2022.

2. Section 4.1(a) of the Plan is hereby deleted and replaced in its entirety with the following:

(a) Subject to adjustment as provided in Section 4.2, the maximum number of shares of Common Stock that shall be available for grant of Awards under the Plan, as of May 31, 2012, shall not exceed 2,100,000 shares. If an Award granted under the Plan, including Awards granted and outstanding as of the Amendment Effective Date, expires, is forfeited or becomes unexercisable for any reason without having been exercised in full, the undelivered shares of Common Stock which were subject to the Award shall, unless the Plan shall have been terminated, become available for future Awards under the Plan.

3. Section 4.3(f) of the Plan is hereby deleted and replaced in its entirety with the following:

(f) Payment of Exercise Price and Withholding Taxes. The number of shares available for grant of Awards under the Plan shall not be increased by (i) the number of shares of Common Stock delivered or withheld to pay the exercise price of any Award, or (ii) the number of shares of Common Stock delivered or withheld to pay withholding taxes payable upon exercise, vesting or payment of any Award.

4. Except as set forth above, the Plan shall continue to read in its current state.

IN WITNESS WHEREOF, Approach has caused the execution of this Second Amendment by its duly authorized officer, effective as of the Amendment Effective Date.

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