Exhibit 99.1

CLAYTON WILLIAMS ENERGY, INC.

FOR IMMEDIATE RELEASE

Thursday, March 31, 2016

CLAYTON WILLIAMS ENERGY ANNOUNCES CHANGES

TO ITS BOARD OF DIRECTORS

Midland, Texas, March 31, 2016 (BUSINESS WIRE) - Clayton Williams Energy, Inc. (the “Company”) (NYSE:CWEI) today announced the resignation of Robert L. Parker from the Company’s Board of Directors (the “Board”) effective March 30, 2016.  Mr. Parker had served as a director of the Company since 1993 and at the time of his resignation served as chairman of the audit committee and served on the compensation committee and the nominating and governance committee.

“We are grateful to Bob for his leadership and service to our Company,” stated Clayton W. Williams, Jr., the Company’s Chairman of the Board.  “Bob’s vast experience in leading a large public company like Parker Drilling for over 50 years made him an excellent Board member, and his integrity and character make him a great man.  We have asked Bob to continue to serve in an advisory, non-voting Board capacity in recognition of his past service as a member of our Board.”

The Company also announced the appointments of Nathan W. Walton and P. Scott Martin to its Board, effective immediately.  Mr. Walton and Mr. Martin were appointed to the Board in connection with the previously announced transaction with funds managed by Ares Management, L.P. (NYSE:ARES).

Clayton Williams Energy, Inc. is an independent energy company located in Midland, Texas.

This release contains forward-looking statements within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934.  All statements, other than statements of historical or current facts, that address activities, events, outcomes and other matters that we plan, expect, intend, assume, believe, budget, predict, forecast, project, estimate or anticipate (and other similar expressions) will, should or may occur in the future are forward-looking statements.  These forward-looking statements are based on management’s current belief, based on currently available information, as to the outcome and timing of future events.  The Company cautions that its future natural gas and liquids production, revenues, cash flows, liquidity, plans for future operations, expenses, outlook for oil and natural gas prices, timing of capital expenditures and other forward-looking statements are subject to all of the risks and uncertainties, many of which are beyond our control, incident to the exploration for and development, production and marketing of oil and gas.

These risks include, but are not limited to, the possibility of unsuccessful exploration and development drilling activities, our ability to replace and sustain production, commodity price volatility, domestic and worldwide economic conditions, the availability of capital on economic terms to fund our capital expenditures and acquisitions, our level of indebtedness, the impact of the current economic recession on our business operations, financial condition and ability to raise capital, declines in the value of

our oil and gas properties resulting in a decrease in our borrowing base under our credit facility and impairments, the ability of financial counterparties to perform or fulfill their obligations under existing agreements, the uncertainty inherent in estimating proved oil and gas reserves and in projecting future rates of production and timing of development expenditures, drilling and other operating risks, lack of availability of goods and services, regulatory and environmental risks associated with drilling and production activities, the adverse effects of changes in applicable tax, environmental and other regulatory legislation, and other risks and uncertainties are described in the Company’s filings with the Securities and Exchange Commission.  The Company undertakes no obligation to publicly update or revise any forward-looking statements.

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