Exhibit 99.1

Alta Mesa Holdings, LP

ALTA MESA ANNOUNCES FIRST QUARTER 2012

FINANCIAL RESULTS AND OPERATIONAL UPDATE

Houston, Texas – May 15, 2012 – Alta Mesa Holdings, LP announced its financial results for the first quarter of 2012 and provided highlights of its recent operations. A conference call to discuss these results is scheduled for today at 2 pm Central time.

Financial and operational highlights of note include the following:

EBITDAX

EBITDAX for the first quarter of 2012 was $47.7 million, up slightly compared to $45.0 million for the first quarter of 2011. The increase in EBITDAX between the two periods was due to increased average price realizations per Mcfe and further movement towards higher margin oil production, all offset by decreased gas production, increased general and administrative costs and workover expenses. EBITDAX for the second quarter of 2012 is expected to range between $48 and $52 million.

Production

Production volumes for the first quarter of 2012 totaled 9.5* billion cubic feet of gas equivalent (“Bcfe”), or an average of 104 million cubic feet of natural gas equivalent per day (“MMcfe/d”), down slightly compared to 9.8 Bcfe or 109 MMcfe/d for the first quarter of 2011. Production for the first quarter is within the previously provided guidance for Q1-2012 of 101 to 105 MMcfe/d. Alta Mesa is continuing its program of a progressive shift of its production mix to a greater proportion of higher margin oil and liquids production located in the Eagle Ford Shale, South Louisiana, Oklahoma and East Texas. The Company’s total production mix has moved to 32% liquids for the first quarter 2012, which is up from 25% liquids production for the same quarter of 2011. We expect this level to move to 40% by the end of the year. Production for the second quarter of 2012 is expected to range between 100 and 104 MMcfe/d.

Revenue & Hedging

Oil and gas revenues for the first quarter of 2012 totaled $78.3 million, up $7.7 million, or 11% compared to oil and gas revenues of $70.6 million for the first quarter of 2011. The variance between the two periods for oil and gas revenues was due primarily to the progressive shift in the Company’s production mix, which has moved to a greater percentage of oil and liquids.

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In order to maximize the downside price protection and minimize any upside price constraints, Alta Mesa actively manages a portfolio of financial swaps and options and takes positions as far as five years into the future. At the end of the first quarter, Alta Mesa had approximately 96% of its proved developed producing reserves volumes hedged for the next five years at average floor prices of over $4.78 for gas and over $99.20 for oil. The net realized gains resulting from the Company’s active management of its oil and gas hedge portfolio were approximately $7.1 million for the first quarter of 2012 compared to $4.3 million for the first quarter of 2011.

Lease Operating Expense

Total lease operating expense, inclusive of production and ad valorem taxes and workover expenses, for the first quarter of 2012 was $23.4 million compared to $20.4 million for the first quarter of 2011. Workover expenses for the first quarter were slightly higher than expected, in part, because of an unscheduled replacement of the defective plastic coated tubing in several wells located in the Urbana field. Additionally, ad valorem taxes related to Alta Mesa’s non-operated interest in the Eagle Ford Shale wells were higher than anticipated.

Depreciation, Depletion and Amortization

Depreciation, depletion and amortization expense for the first quarter of 2012 was $23.9 million compared to $19.5 million for the first quarter of 2011. On a per Mcfe basis, depreciation, depletion and amortization expense for the first quarter was $2.47 per Mcfe compared to $1.99 per Mcfe for the first quarter of 2011.

General and Administrative Expenses

General and administrative expenses for the first quarter of 2012 were $8.0 million compared to $5.8 million for the first quarter of 2011. The increase in general and administrative expenses between the periods was primarily the result of increased salary expense due to additional personnel, as well as increased consulting fees for engineering services and legal fees.

Net Income

Net income for the first quarter of 2012 was $3.4 million, compared to a net loss of $12.2 million for the first quarter of 2011. The net income for the first quarter was up by $15.6 million compared to the first quarter of 2011, primarily due to higher oil revenues between the quarters. This is a result of the continued execution of Alta Mesa’s production mix shift to a greater proportion of higher margin oil and liquids, offset in part by higher lease operating expense and general and administrative expense.

Borrowing Base Increased

Alta Mesa’s lenders have completed the semi-annual redetermination of the Company’s borrowing base under its senior secured revolving credit facility. Pursuant to the terms of the reserve-based revolving line of credit facility, the borrowing base has been increased by the lenders to $350 million. This represents an increase of 8%, or $25 million over the previous level of $325 million. At the end of the first quarter, the Company had $207 million in borrowings outstanding under the facility. Alta Mesa is in compliance with all of the financial covenants associated with the credit facility and the next scheduled redetermination of the borrowing base is November 1, 2012. The credit facility is available to provide funds for the exploration, development and/or acquisition of oil and gas properties and for working capital and other general corporate purposes. The credit facility is provided by a syndicate of nine banks agented by Wells Fargo Bank, N.A. and co-agented by Union Bank, N.A.

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

Operational Highlights

South Louisiana:

The Company continues to develop its South Louisiana assets, the most significant of which is Weeks Island oil field. This historically prolific salt dome oil field, which has over 50 potential pay zones, offers significant opportunities for added production and reserves. Located in Iberia Parish, Louisiana, Weeks Island contains some of Alta Mesa’s largest developed oil reserves. Alta Mesa has continuously employed one drilling rig and one completion rig in this field since mid-2011, resulting in twelve successful oil producing wells in addition to several recompletions. Alta Mesa operates all of the wells in this field in which it has a working interest. Weeks Island oil sales contracts are based on the Louisiana Light Sweet crude market price index, which has been consistently higher than the West Texas Intermediate index in 2012.

Eagle Ford Shale:

Alta Mesa’s Eagle Ford Shale assets are principally operated by Murphy Oil in the oil and liquids-rich window of the play in Karnes County. Murphy is currently operating three drilling rigs on our joint acreage. Alta Mesa’s reserves and daily production have grown significantly over the past year in this area. At the end of the first quarter, the Company had working interests in 27 producing wells and overriding royalty interests in three additional wells. The total number of proposed wells in the program could increase depending on decisions for downspacing. The crude sold from this field currently receives an average of $6 to $9 per barrel premium over the West Texas Intermediate index price. Lease operating costs continue to show improvement as a result of the conversion of temporary infrastructure to more permanent infrastructure. Net production from this area has increased by 26% from an average daily production rate in fourth quarter 2011 of 1,338 barrels of oil equivalent (“BOE”), to an average daily production rate in the first quarter 2012 of 1,685 BOE. Production at the end of April 2012 was approximately 2,000 BOE per day, net to Alta Mesa’s interest.

East Texas Area:

In East Texas, Alta Mesa is focused on the exploitation of multiple oil and liquids-rich natural gas opportunities in the Wilcox, Woodbine, Eagle Ford and Austin Chalk formations, including the use of horizontal drilling. The Company is participating in a Woodbine/Eagle Ford drilling program with EnCana. In the Hilltop field, three horizontal wells were drilled from the same pad during the first quarter. Two wells penetrated one Woodbine interval and a third well was drilled into a lower Woodbine sand, after which, all three laterals had multi-stage fracture stimulations. Alta Mesa has a 26% working interest in these wells. Additionally, Alta Mesa recently completed its first operated well in the area, which was a successful horizontal oil well in the Austin Chalk formation. Alta Mesa intends to pursue opportunities in other prospective and productive formations in the area such as the Buda, Glen Rose and Pettet.

Oklahoma:

Capital expenditures in Oklahoma are expected to increase from $8 million in 2011 to approximately $20 million in 2012 as the Company continues to shift its focus to oil and liquids-rich gas projects. Alta Mesa’s assets in Oklahoma are located in Kingfisher County in the Sooner Trend field at depths that range from less than 5,000 feet to 8,000 feet in multiple pay zones. Alta Mesa owns working interests in five large production units and is engaged in what it believes is a low-risk and low-cost program to improve oil production from several zones, including the Mississippian Lime formation. This is being accomplished by deepening and testing multiple existing wells and then evaluating these wellbores for additional exploitation potential, including the use of horizontal drilling. Alta Mesa believes that, at a

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

minimum, it can retrieve an additional 30,000 barrels of oil with each well that is deepened into the Mississippian Lime formation. This would provide the Company with meaningful upside for future incremental development in this long-lived oil field.

Conference Call Information

Alta Mesa invites you to listen to its conference call which will discuss its financial and operational results at 2:00 p.m., Central time, on Tuesday, May 15, 2012. If you wish to participate in this conference call, dial 877-317-6789 (toll free in US/Canada) or 412-317-6789 (for International calls), five to ten minutes before the scheduled start time and reference Conference ID # 10014171. A webcast of the call and any related materials will be available on Alta Mesa’s website at www.altamesa.net. Additionally, a replay of the conference call will be available for one week following the live broadcast by dialing 877-344-7529 (toll free in US/Canada) or 412-317-0088 (International calls), and referencing Conference ID # 10014171.

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 of 1933, as amended, 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. 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. Forward-looking statements may include statements about Alta Mesa’s: business strategy; reserves; financial strategy, liquidity and capital required for our development program; realized oil and natural gas prices; timing and amount of future production of oil and natural gas; hedging strategy and results; future drilling plans; competition and government regulations; marketing of oil and natural gas; leasehold or business acquisitions; costs of developing our properties; general economic conditions; credit markets; liquidity and access to capital; uncertainty regarding our future operating results; and plans, objectives, expectations and intentions contained in this press release that are not historical. We caution 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 our 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, lack of availability of drilling and production equipment and services, environmental risks, 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. 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, our 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.

FOR MORE INFORMATION CONTACT: Lance L. Weaver (281) 943-5597 lweaver@altamesa.net

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF OPERATIONS

(unaudited)

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

(dollars in thousands)

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED STATEMENT OF CASH FLOWS

(unaudited—dollars in thousands)

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net

GAAP to Non-GAAP Reconciliation

Adjusted EBITDAX is a non-GAAP financial measure and as used herein represents net income before interest expense, exploration expense, depletion, depreciation and amortization, impairment of oil and natural gas, accretion of asset retirement obligations, deferred tax expense, unrealized gain/loss on oil and natural gas derivative contracts and unrealized gain/loss on warrants. We present Adjusted EBITDAX because we believe it is an important supplemental measure of our performance that is frequently used by others in evaluating companies in our industry. Adjusted EBITDAX is not a measurement of our financial performance under GAAP, and should not be considered as an alternative to net income, operating income or any other performance measure derived in accordance with GAAP or as an alternative to net cash provided by operating activities as a measure of our profitability or liquidity. Adjusted EBITDAX has significant limitations, including that it does not reflect our cash requirements for capital expenditures, contractual commitments, working capital or debt service. In addition, other companies may calculate Adjusted EBITDAX differently than we do, limiting its usefulness as a comparative measure.

The following table sets forth a reconciliation of net income (loss) as determined in accordance with GAAP to Adjusted EBITDAX for the periods indicated:

*Production Volumes: Production Month versus Accounting Month

Alta Mesa provides quarterly “production month” volume guidance based on the anticipated forthcoming production and then reports the actual “production month” volumes in its quarterly earnings press release so that the market can note how the company performed relative to its stated guidance. The volume amounts reported in the Company’s quarterly reports on Form 10-Q filed with the Securities and Exchange Commission show the “accounting month” volumes which incorporate prior period adjustments. These amounts generally differ slightly from the “production month” volumes reported in the press release.

The “accounting month” production volumes for the first quarter of 2012 totaled 9.7 Bcfe, or an average of 106 MMcfe/d.

15021 Katy Freeway, Suite 400    —    Houston, Texas 77094    —    (281) 530-0991    —    www.altamesa.net