ENERGY & EXPLORATION PARTNERS, INC. 2012 STOCK INCENTIVE PLAN SECOND AMENDMENT TO RESTRICTED STOCK AWARD AGREEMENT

Exhibit 10.42

ENERGY & EXPLORATION PARTNERS, INC.

2012 STOCK INCENTIVE PLAN

SECOND AMENDMENT TO RESTRICTED STOCK AWARD AGREEMENT

THIS SECOND AMENDMENT TO RESTRICTED STOCK AWARD AGREEMENT, dated as of December 1, 2013 (this “Amendment”), is made by and between Energy & Exploration Partners, Inc., a Delaware corporation (the “Company”), and Brian Nelson (the “Participant”). Capitalized terms used herein but not otherwise defined shall have the meanings ascribed thereto in the Agreement (as defined below).

RECITALS:

WHEREAS, the Company adopted the Energy & Exploration Partners, Inc. 2012 Stock Incentive Plan (the “Plan”) pursuant to which awards of Restricted Stock of the Company may be granted; and

WHEREAS, the Company and the Participant entered into that certain Restricted Stock Award Agreement, dated August 22, 2012 (the “Agreement”); and

WHEREAS, the Company and the Participant entered into that certain First Amendment to Restricted Stock Award Agreement, dated November 16, 2012, for the purpose of amending certain terms and provisions of the Agreement; and

WHEREAS, the Committee has determined that it is in the best interests of the Company and its stockholders to enter into this Amendment with the Participant in recognition of the Participant’s services to the Company and to align the Participant’s and Company’s interests, subject to the terms set forth herein.

NOW, THEREFORE, in consideration for the services rendered by the Participant to the Company and the mutual covenants hereinafter set forth, the parties hereto agree as follows:

I. AMENDMENTS

“4. Vesting. Except as otherwise provided herein, the restrictions described in Section 3 above will lapse with respect to a percentage of the Restricted Shares on the dates set forth herein (each a “Vesting Date,” and, with respect to each Restricted Share, the period beginning on the Date of Grant and ending on the applicable Vesting Date for such share, the “Restricted Period”); provided that the Participant is still in Continuous Service with the Company on each such Vesting Date. The Vesting Date shall be March 31, 2014. On the Vesting Date, the restrictions described in Section 3 above will lapse with respect to 100% of the Restricted Shares.”

II. MISCELLANEOUS

(a) Governing Law. This Amendment shall be construed and interpreted in accordance with the laws of the State of Delaware without regard to principles of conflicts of law thereof, or principles of conflicts of laws of any other jurisdiction that could cause the application of the laws of any jurisdiction other than the State of Delaware.

(a) Severability. Every provision of this Amendment is intended to be severable and any illegal or invalid term shall not affect the validity or legality of the remaining terms.

(b) Headings. The headings of the Sections hereof are provided for convenience only and are not to serve as a basis for interpretation of construction, and shall not constitute a part of this Amendment.

(c) Effect of Amendment; Agreement Continuation. Except as amended hereby, all other terms and conditions of the Agreement shall remain the same and in full force and effect. The Agreement, as modified herein, shall continue in full force and effect, and nothing herein contained shall be construed as a modification of existing rights under the Agreement, except as such rights are expressly modified hereby.

(d) Counterparts. This Amendment may be signed in counterparts (including by facsimile transmission), each of which shall be deemed an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

[Signature page follows]

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IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the day first written above.

The undersigned hereby accepts the terms of this Amendment.

Signature page to Second Amendment to Restricted Stock Award Agreement