Form of Lock-Up Agreement from the stockholders of Blue Ridge Mountain Resources, Inc. party thereto

Exhibit 10.4

LOCK-UP AGREEMENT

August 25, 2018

Eclipse Resources Corporation

2121 Old Gatesburg Road, Suite 110

State College, Pennsylvania 16803

Blue Ridge Mountain Resources, Inc.

122 West John Carpenter Freeway, Suite 300

Irving, Texas 75039

Ladies and Gentlemen:

Reference is hereby made to the Agreement and Plan of Merger (the “Merger Agreement”), dated August 25, 2018, among Eclipse Resources Corporation, a Delaware corporation (“Parent”), Blue Ridge Mountain Resources, Inc., a Delaware corporation (the “Company”), and Everest Merger Sub Inc., a Delaware corporation (“Merger Sub”). The Merger Agreement provides that, among other things, (i) Merger Sub will merge with and into the Company (the “Merger”), and (ii) each share of the common stock, par value $0.01 per share, of the Company (the “Company Common Stock”) issued and outstanding immediately prior to the effective time of the Merger shall be converted into the right to receive a number of shares of common stock, par value $0.01, of Parent (the “Parent Common Stock”), all as set forth in the Merger Agreement. It is expected that, as a holder of Company Common Stock, if the Merger becomes effective, each of the undersigned will receive shares of Parent Common Stock in the Merger.

Each of the undersigned is entering into this letter agreement (this “Lock-Up Agreement”) to induce Parent and the Company to enter into the Merger Agreement.

Each of the undersigned agrees that, without Parent’s prior written consent, but subject to the provisions of the next following paragraph, the undersigned will not, for a period commencing at the effective time of the Merger and ending at midnight on the sixtieth (60th) day thereafter (the “Lock-Up Period”), directly or indirectly (1) offer, pledge, sell, contract to sell, grant any option or contract to purchase, purchase any option or contract to sell, or otherwise dispose of, any shares of Parent Common Stock or any securities convertible into, exercisable for, or exchangeable for shares of Parent Common Stock, (2) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of Parent Common Stock, whether any such transaction described in clause (1) or (2) above is to be settled by

delivery of Parent Common Stock or such other securities, in cash or otherwise, or (3) publicly announce an intention to do any of the foregoing.

The restrictions in the foregoing paragraph shall not apply to:

provided, however, that in each transfer pursuant to clause (b), prior to such transfer the transferee agrees in writing (in form and substance acceptable to Parent) to be bound by the terms of this Lock-Up Agreement and such transfer shall not involve a disposition for value; and provided further, that in each transfer pursuant to clause (b) and (c), no publicly available filing or public announcement is required or voluntarily made by any party in connection with such transfer.

Each of the undersigned also agrees and consents to the entry of stop transfer instructions with Parent’s transfer agent and registrar relating to the transfer of the undersigned’s shares of Parent Common Stock except in compliance with the restrictions described above.

Each of the undersigned also agrees that, during the period from the date of this Lock-Up Agreement to the effective time of the Merger, the undersigned will not make any Permitted Transfer of Subject Securities (each as defined in the Voting Agreement dated as of the date hereof among the undersigned, certain other holders or beneficial owners of Company Common Stock, Parent and the Company (the “Voting Agreement”)) unless, prior to such Permitted Transfer, the transferee in such Permitted Transfer agrees in writing (in form and substance acceptable to Parent and the Company) to be bound by the terms of this Lock-Up Agreement.

This Lock-Up Agreement shall not be amended or modified except by an instrument in writing executed by Parent, the undersigned and, prior to the effective time of the Merger, the Company. This Lock-Up Agreement shall be governed by and

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construed in accordance with the laws of the State of Delaware, without regard to the conflict of laws principles thereof.

Each of the undersigned understands that the Company, Parent and other stockholders of the Company are relying on this Lock-Up Agreement in proceeding with the Merger. This Lock-Up Agreement is irrevocable and shall be binding upon the undersigned and the heirs, personal representatives, successors and assigns of the undersigned.

Notwithstanding anything herein to the contrary, this Lock-Up Agreement shall be effective and binding on the undersigned only if, on or before the date of the Merger Agreement, Parent and the Company shall have received an executed lock-up agreement from each of (i) the other holders or beneficial owners of Company Common Stock listed on Exhibit A hereto and (ii) EnCap Energy Capital Fund VIII, L.P., EnCap Energy Capital Fund VIII Co-Investors, L.P. and EnCap Energy Capital Fund IX, L.P., pursuant to which each of them has agreed to restrictions on transfer of shares of Parent Common Stock on substantially the same terms as (or terms no more favorable to such entities than) those set forth in this Lock-Up Agreement, except as noted on Exhibit A.

[Signatures appear on the following pages.]

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Signature to come

EXHIBIT A

OTHER HOLDERS OR BENEFICIAL OWNERS OF

COMPANY COMMON STOCK EXECUTING LOCK-UPS

Goldman Sachs Asset Management, L.P., on behalf of its participating funds and accounts listed under its name on Schedule A to the Voting Agreement*

Western Asset Management Company, LLC, as investment manager and agent for the stockholders listed under its name on Schedule A to the Voting Agreement

Specialty Loan Fund III, L.P.

Specialty Loan Sector D Investment Fund, L.P.

Specialty Loan Institutional Holdings DAC

Specialty Loan Institutional Fund III, L.P.

Specialty Loan VG Fund, L.P.

NDT Senior Loan Fund L.P.

Aiguilles Rouges Sector A Investment Fund, L.P.