SECOND SUPPLEMENTAL INDENTURE

Exhibit 4.1

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE (this “Second Supplemental Indenture”), dated as of December 20, 2016, between Approach Resources, Inc., a Delaware corporation (the “Company”), the Guarantors (as hereinafter defined) and Wilmington Trust, National Association, as successor trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H

WHEREAS, the Company and the guarantors party thereto (the “Guarantors”) delivered to the Trustee a base indenture, dated as of June 11, 2013 (the “Base Indenture”), by and among the Company, the guarantors party thereto and the Trustee, as supplemented by the First Supplemental Indenture dated as of June 11, 2013 (the “First Supplemental Indenture” and, together with the Base Indenture, the “Indenture”) providing for the issuance by the Company of a series of senior notes designated as 7.00% Senior Notes due 2021 (the “Notes”);

WHEREAS, pursuant to that certain Exchange Agreement, dated as of the date hereof (the “Exchange Agreement”), by and between the Company and Wilks Brothers, LLC, a Texas limited liability company, and SDW Investments, LLC, a Texas limited liability company (the “Noteholders”), the Company and the Noteholders have reached an agreement pursuant to which, amongst other things, upon satisfaction of the conditions to closing set forth therein, the Noteholders will transfer to the Company, and the Company shall acquire, directly or indirectly, all of the Notes held by the Noteholders in exchange for, shares of Common Stock (as defined in the Exchange Agreement) of the Company (the “Exchange”);

WHEREAS, in connection with the Exchange Agreement, the Noteholders have delivered one or more consent letters executed by Cede & Co, the registered Holder of the Notes, on behalf of the Noteholders (collectively, the “Noteholder Consents”) to supplement the Indenture to effect the amendments set forth in Sections 2, 3, 4 and 5 hereof (collectively, the “Amendments”) on the terms set forth herein, including that this Second Supplemental Indenture shall be in full force and effect on the date first written above and such Amendments shall become operative with respect to the Indenture only if the Closing (as defined in the Exchange Agreement) shall occur (such Closing, the “Operative Time”);

WHEREAS, subject to certain exceptions, Section 1002 of the First Supplemental Indenture provides, among other things, that the Company, the Guarantors and the Trustee may amend or supplement the Indenture, the Securities Guarantees and the Notes (and the Company and the Guarantors desire to amend and supplement the Indenture, the Securities Guarantees and the Notes as provided herein) with the consent of the Holders of at least a majority in aggregate principal amount of the Notes then outstanding voting as a single class;

WHEREAS, the Noteholders beneficially own $130,552,000, or 56.7% of the $230,200,000 aggregate principal amount of the issued and outstanding Notes, Cede & Co. has executed the Noteholder Consents in respect of such aggregate principal amount, and accordingly the Holder of at least a majority in aggregate principal amount of the outstanding Notes for the purposes of Section 1002 of the First Supplemental Indenture has duly consented to this Second Supplemental Indenture; and

WHEREAS, all conditions necessary to authorize the execution and delivery of this Second Supplemental Indenture and to make this Second Supplemental Indenture valid and binding have been complied with or performed.

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NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company, the Guarantors, and the Trustee mutually covenant and agree for the equal and ratable benefit of the holders of the Notes as follows:

1. CAPITALIZED TERMS. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2. AMENDMENTS TO SECTION 201 OF THE FIRST SUPPLEMENTAL INDENTURE. Section 201 of the First Supplemental Indenture is hereby amended at the Operative Time by deleting those definitions and cross references that, by virtue of the amendments effected in Sections 3, 4 and 5 hereof, are no longer used in the Indenture or the Notes.

3. AMENDMENTS TO SECTION 601 OF THE FIRST SUPPLEMENTAL INDENTURE.

(a) Each of the following clauses of Section 601 of the First Supplemental Indenture is hereby deleted in their entirety at the Operative Time and each such clause is replaced at such time with the following: “[Intentionally Omitted]” (and all references thereto in the Indenture are hereby deleted in their entirety) at such time:

(b) (i) Clause (3) of Section 601 of the First Supplemental Indenture is hereby amended at the Operative Time to delete the phrase “or to consummate a purchase of Notes when required pursuant to Section 1110 or Section 1115 of this Supplemental Indenture”; and (ii) each of clause (9) and clauses (10)(a), (b), and (c) of Section 601 of the First Supplemental Indenture is hereby amended at the Operative Time to delete the following phrase, each time it appears therein: “, any Significant Subsidiary or any group of Restricted Subsidiaries that, taken together (as of the latest audited consolidated financial statements for the Company and its Restricted Subsidiaries), would constitute a Significant Subsidiary,”.

4. AMENDMENTS TO SECTION 901 OF THE FIRST SUPPLEMENTAL INDENTURE.

Each of clauses (3) and (4) of Section 901 of the First Supplemental Indenture is hereby deleted in its entirety at the Operative Time and each such clause is replaced at such time with the following: “[Intentionally Omitted]” (and all references thereto in the Indenture are hereby deleted in their entirety at such time), and the proviso at the end of the first paragraph of Section 901 is hereby deleted in its entirety at such time.

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5. AMENDMENTS TO ARTICLE 11 OF THE FIRST SUPPLEMENTAL INDENTURE. Each of the following sections of the First Supplemental Indenture is hereby deleted in its entirety at the Operative Time and each such section is replaced at such time with the following: “[Intentionally Omitted]” (and all references thereto in the Indenture are hereby deleted in their entirety at such time):

6. NEW YORK LAW TO GOVERN. THE LAWS OF THE STATE OF NEW YORK WILL GOVERN AND BE USED TO CONSTRUE THIS SECOND SUPPLEMENTAL INDENTURE WITHOUT GIVING EFFECT TO APPLICABLE PRINCIPLES OF CONFLICTS OF LAW TO THE EXTENT THAT THE APPLICATION OF THE LAWS OF ANOTHER JURISDICTION WOULD BE REQUIRED THEREBY.

7. COUNTERPARTS. The parties may sign any number of copies of this Second Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement.

8. EFFECT OF HEADINGS. The Section headings herein are for convenience only and shall not affect the construction hereof.

9. INCORPORATION OF INDENTURE. All the provisions of this Second Supplemental Indenture shall be deemed to be incorporated in, and made a part of, the Indenture; and the Indenture, as supplemented and amended by this Agreement, shall be read, taken and construed as one and the same instrument.

10. THE TRUSTEE. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Second Supplemental Indenture or for or in respect of the recitals contained herein.

11. EFFECTIVENESS OF THIS SECOND SUPPLEMENTAL INDENTURE. Upon the execution of this Second Supplemental Indenture by the Company, the Guarantors, and the Trustee, the Indenture shall

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be amended and supplemented in accordance herewith, and this Second Supplemental Indenture shall form a part of the Indenture for all purposes, and the parties hereto and every Holder of Notes shall be bound hereby; provided, however, that the Amendments will not become effective and operative unless and until the Operative Time shall have occurred, at which time such Amendments shall immediately become effective and operative for all purposes of the Indenture without further action by any Person, and simultaneously therewith the Notes and the Securities Guarantees shall be deemed supplemented and amended for all purposes, as and to the same extent as the Indenture has been supplemented and amended hereby. In the event that the Exchange Agreement is terminated without the Closing having occurred, the Amendments will not become effective and operative, and this Supplemental Indenture shall immediately upon such termination be of no further force or effect. The Company shall give the Trustee prompt written notice of the occurrence of the Operative Time or the termination of the Exchange Agreement. For the avoidance of doubt, nothing in this Second Supplemental Indenture shall effect in any way the deletion and replacement, or intentional omission, of any Article, Section, clause or other provision of the Base Indenture specified in Section 102 of the First Supplemental Indenture, which Section 102 shall remain in full force and effect subject only to the amendments specified in this Second Supplemental Indenture, or amend the Base Indenture as it may apply to any Securities other than the Notes.

[Signature pages follow]

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IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental Indenture to be duly executed and delivered, all as of the date first above written.

[SIGNATURE PAGE TO SECOND SUPPLEMENTAL INDENTURE]

IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental Indenture to be duly executed and delivered, all as of the date first above written.

[SIGNATURE PAGE TO SECOND SUPPLEMENTAL INDENTURE]