Exhibit 99.1

Alta Mesa Holdings, LP Announces Early Participation Time Extension

HOUSTON, TEXAS, March 2, 2016 – Alta Mesa Holdings, LP (“Alta Mesa” or the “Company”) today announced that the Early Participation Time in relation to its private offer to exchange (the “Exchange Offer”) any and all of its outstanding 9 5/8% senior notes due 2018 (the “Notes”) held by eligible holders, for new 10 5/8% senior secured third lien term loans of Alta Mesa maturing in 2021 (the “Term Loans”) has been further extended from 5:00 p.m. New York City time on March 1, 2016 to 5:00 p.m. New York City time on March 4, 2016. The Withdrawal Deadline for the Exchange Offers has passed, and therefore any Notes tendered in the Exchange Offer may no longer be withdrawn (and the related consents to certain proposed amendments to the indenture governing the Notes may no longer be revoked).

The terms and conditions of the Exchange Offer are detailed in a confidential offer to exchange and consent solicitation statement and a related letter of transmittal, each dated February 11, 2016 (together, the “Offer to Exchange and Solicitation Statement”). This announcement should be read in conjunction with the initial announcement of the Exchange Offer by Alta Mesa, dated February 11, 2016.

The Exchange Offer will expire at 11:59 p.m., New York City time, on March 10, 2016, unless extended by Alta Mesa (the “Expiration Time”). The consummation of the Exchange Offer is subject to, and conditioned upon, the satisfaction or waiver of conditions set out in the Offer to Exchange and Solicitation Statement. The consummation of the Exchange Offer is also subject to Alta Mesa’s right to amend the Exchange Offer prior to the Expiration Time. The Exchange Offer is not subject to any minimum amount of Notes being tendered.

This press release is for informational purposes only. This press release shall not constitute an offer to exchange, nor a solicitation of an offer to exchange any security. No recommendation is being made as to whether holders of the Notes should exchange Notes for Term Loans.

Alta Mesa Holdings, LP is a privately held company engaged primarily in onshore oil and natural gas acquisition, exploitation, exploration and production whose focus is to maximize the profitability of our assets in a safe and environmentally sound manner. We seek to maintain a portfolio of lower risk properties in plays with known resources where we identify a large inventory of lower risk drilling, development, and enhanced recovery and exploitation opportunities. We maximize the profitability of our assets by focusing on sound engineering, enhanced geological techniques including 3-D seismic analysis, and proven drilling, stimulation, completion, and production methods. Alta Mesa Holdings, LP is headquartered in Houston, Texas.

Safe Harbor Statement and Disclaimer

This press release includes “forward-looking statements” within the meaning of Section 27A of the Securities Act, and Section 21E of the Securities Exchange Act of 1934, as amended. All statements, other than statements of historical fact, regarding Alta Mesa’s strategy, future operations, financial position, estimated revenues and losses, projected costs, prospects, plans and objectives of management are forward-looking statements. When used in this press release, the words “could”, “should”, “will”, “play”, “believe”, “anticipate”, “intend”, “estimate”, “expect”, “project” and similar expressions are intended to identify forward-looking statements, although not all forward-looking statements contain such identifying words. These forward-looking statements are based on Alta Mesa’s current expectations and assumptions about future events and are based on currently available information as to the outcome and timing of future events. Forward-looking statements may include statements about Alta Mesa’s: business strategy; reserves quantities and the present value of its reserves; financial strategy, liquidity and capital required for its development program; future realized oil and natural gas prices; timing and amount of

future production of oil and natural gas; hedging strategy and results; future drilling plans; marketing of oil and natural gas; leasehold or business acquisitions; costs of developing its properties; liquidity and access to capital; uncertainty regarding its future operating results; and plans, objectives, expectations and intentions contained in this press release that are not historical. Alta Mesa cautions you that these forward-looking statements are subject to all of the risks and uncertainties, most of which are difficult to predict and many of which are beyond its control, incident to the exploration for and development and production of oil and natural gas. These risks include, but are not limited to, commodity price volatility, low prices for oil and/or natural gas, global economic conditions, inflation, increased operating cost, lack of availability of drilling and production equipment and services, environmental risks, weather risk, drilling and other operating risks, regulatory changes, the uncertainty inherent in estimating oil and natural gas reserves and in projecting future rates of production, cash flow and access to capital, the timing of development expenditures, and other risks. Reserve engineering is a process of estimating underground accumulations of oil and natural gas that cannot be measured in an exact way. The accuracy of any reserve estimate depends on the quality of available data, the interpretation of such data and price and cost assumptions made by reservoir engineers. Specifically, future prices received for production and costs may vary, perhaps significantly, from the prices and costs assumed for purposes of these estimates. Prices for oil or gas began a severe decline in the third quarter of 2014 and remain depressed as of the date of this press release. Sustained lower prices will cause the twelve month weighted average price to decrease over time as the lower prices are reflected in the average price, which may result in the estimated quantities and present values of Alta Mesa’s reserves being reduced. In addition, the results of drilling, testing and production activities may justify revisions of estimates that were made previously. If significant, such revisions would change the schedule of any further production and development drilling. Accordingly, reserve estimates may differ significantly from the quantities of oil and natural gas that are ultimately recovered. Should one or more of the risks or uncertainties described in this press release occur, or should underlying assumptions prove incorrect, Alta Mesa’s actual results and plans could differ materially from those expressed in any forward-looking statements. All forward-looking statements, expressed or implied, included in this press release are expressly qualified in their entirety by this cautionary statement. This cautionary statement should also be considered in connection with any subsequent written or oral forward-looking statements that we may issue. Except as otherwise required by applicable law, we disclaim duty to update any forward-looking statements, all of which are expressly qualified by the statements in this section, to reflect events or circumstances after the date of this press release.