EXHIBIT 99.1

THE MERIDIAN RESOURCE CORPORATION ANNOUNCES FIRST QUARTER
FINANCIAL RESULTS AND SHAREHOLDER RIGHTS PLAN

HOUSTON--(BUSINESS WIRE)--May 6, 1999--The Meridian Resource Corporation
(NYSE:TMR) today announced record production and revenues for the first quarter
1999 period. Production increased 142% to 12.4 Bcfe from 5.1 Bcfe during the
first quarter of 1998. The increase is mainly attributable to the acquisition
and the successful development of the Shell properties. Despite the low
commodity price environment, revenues increased 96% to $23.3 million from $11.9
million during the first quarter of 1998, again primarily a result of the
acquisition and development of the Shell properties. Operating cash flow
increased 37% to $7.7 million from $5.6 when compared to the same period.

For the quarter, the Company reported a net loss applicable to common
shareholders of $5.0 million, or $0.11 per share, compared to a net loss of
$40.9 million, or $1.22 per share, during the first quarter of 1998. The current
quarter net loss was a result of lower average commodity prices of $11.44 per
barrel of oil and $1.83 per MCF of natural gas, 16% and 20% decreases,
respectively, compared to realized prices during the same quarter of 1998. Oil
and gas operating expenses for the first quarter were $4.2 million up from $1.5
million for the first quarter 1998. This was due to the addition of the Shell
properties as well as the addition of new wells brought on production during the
last twelve months. On an Mcfe basis, oil and gas operating expenses were
$0.34/Mcfe compared to $0.30/Mcfe during the same period last year. The
$0.04/Mcfe increase was primarily attributable to the increases in the number of
producing wells combined with a shift in the production mix because of the
increased oil production. Severance and ad valorem taxes for the first quarter
of 1999 totaled $2.2 million, an increase of $1.8 million from the same period
in 1998, again as a result of an increase in production and reflecting 84% of
production onshore in the 1999 period (and subject to severance taxes) compared
to 35% onshore production during the same period in 1998. Unit costs per Mcfe
for depletion and depreciation and amortization (D, D&A) have declined to
$1.03/Mcfe, compared to $1.22/Mcfe for the same period in 1998 and $1.31/Mcf for
the fourth quarter of 1998, primarily a result of reserve additions on the Shell
properties and Meridian's Lily Boom prospect in Louisiana.

General and administrative expenses during the first quarter of 1999 totaled
$2.8 million, an increase of $0.8 million over the first quarter of 1998,
related to the increased volume of seismic assets, leases and properties. On a
cost per Mcfe basis, the Company recognized a significant reduction in general
and administrative expenses from $0.39/Mcfe to $0.22/Mcfe compared to the same
quarter a year ago.

Capital expenditures during the first quarter of 1999 totaled $21.9 million and
primarily consisted of exploration and development expenditures at the Company's
North Turtle Bayou/Ramos Field, Weeks Island Field, Thornwell Field, Rockefeller
Refuge prospect, South Timbalier Block 290-291 and Eugene Island Block 304.
These costs were financed primarily by a combination of cash flow from
operations and borrowings under the Company's credit facility. For the balance
of 1999, Meridian's capital budget is focused on low risk development and
exploitation projects, concentrating at the Company's Weeks Island, North Turtle
Bayou/Ramos, Thornwell, Kings Bayou and Rockefeller projects. Since year-end,
the Company has increased its proved reserve position from 304 BCFEq to 358
BCFEq at March 31, 1999, after deducting 12.3 BCFEq of production during the
first quarter.

The Company further announced that its board of directors has adopted a
shareholders rights plan designed to provide additional negotiating leverage to
the Company's board of directors in the event of a unsolicited takeover bid and
to protect the Company's shareholders against inadequate offers. Under the terms
of the rights plan, the Company will distribute one right for each outstanding
share of common stock to holders of record at the close of business on May 17,
1999. The rights plan would be triggered if an acquiring party accumulates 15%
or more of the Company's common stock.

The rights are not being distributed in response to any specific effort to
acquire the Company but to protect the interests of its shareholders in the
event that the Company and its shareholders are confronted with coercive or
unfair takeover tactics. The rights plan is similar to those adopted by numerous
other companies, the details of which will be outlined in a letter that will be
mailed to shareholders.

Certain of the foregoing statements may be deemed "forward-looking statements"
within the meaning of the Securities Exchange Act of 1934. Although Meridian
believes that the expectations reflected in such forward-looking statements are
reasonable; there can be no assurance that such expectations will prove to have
been correct. Certain risks and uncertainties inherent in Meridian's business
are set forth in Meridian's filings with the Securities and Exchange Commission.
These risks include (i) the continued production from existing wells at their
current or projected levels, (ii) price changes for oil and gas, (iii) the
ability of the Company to successfully complete those wells that have been
logged and reflect potential production, (iv) the ability of the Company to
successfully complete and produce those reserves classified as "non-producing"
or "undeveloped", (v) the ability of the Company to acquire leases and timely
drill its exploratory prospects, (vi) risks regarding estimates of reserves,
(vii) production risks, (viii) governmental regulations and (ix) general risks
regarding the exploration for, and production of, oil and gas reserves.

The Meridian Resource Corporation is an independent oil and natural gas company
engaged in the exploration for and development of oil and natural gas properties
utilizing 3-D seismic technology, primarily in south Louisiana, southeast Texas
and offshore Gulf of Mexico. Meridian's office is located in Houston, and the
stock is traded on the New York Stock Exchange under the symbol "TMR."

                   THE MERIDIAN RESOURCE CORPORATION
                 CONSOLIDATED STATEMENTS OF OPERATIONS
                              (UNAUDITED)

                                                          Three months ended
                                                               March 31,
                                                       -------------------------
                                                        1999              1998
                                                       -------           -------
Revenues:
 Oil and natural gas .......................           $23,104           $11,766
 Interest and other ........................               202               131
                                                       -------           -------
                                                        23,306            11,897

Costs and expenses:
 Oil and natural gas operating ...............           4,170            1,518
 Severance and ad valorem taxes ..............           2,239              460
 Depletion and depreciation ..................          12,687            6,259
 General and administrative ..................           2,794            1,977
 Interest ....................................           5,055            2,332
 Impairment of long-lived assets .............            --             40,278
                                                      --------         --------
                                                        26,945           52,824
                                                      --------         --------
Net loss .....................................          (3,639)         (40,927)

Preferred stock dividend .....................          (1,350)            --
                                                      --------         --------
Net loss applicable to
 common stockholders .........................        ($ 4,989)        ($40,927)
                                                      ========         ========
Net loss per share ...........................        ($   .11)        ($  1.22)
                                                      ========         ========
Weighted average common shares
 Outstanding .................................          45,817           33,451


                        THE MERIDIAN RESOURCE CORPORATION
                        FINANCIAL AND OTHER DATA SUMMARY
                                   (UNAUDITED)

                                                                       1999
                                Three months ended      1999        Percentage
                                     March 31,         Increase      Increase
                                 1999        1998      Decrease      Decrease
                               --------    --------    ---------    ----------
                                     (in thousands, except per share data)
Production:
 Oil (MBbls) ................     1,044         210          834           397%
 Natural gas (MMcf) .........     6,109       3,858        2,251            58%
 Natural gas
  equivalent (Mmcfe) ........    12,373       5,118        7,255           142%

Average sales prices:
 Oil ($/Bbl) ................  $  11.44    $  13.65    ($   2.21)          (16%)
 Natural gas ($/Mcf) ........  $   1.83    $   2.29    ($   0.46)          (20%)
 Natural gas
  equivalent ($/Mcfe) .......  $   1.87    $   2.29    ($   0.42)          (18%)

Net loss(a) .................  ($ 4,989)   ($40,927)        --            --
Net loss per share(a) .......  ($   .11)   ($  1.22)        --            --
Cash flow(b) ................  $  7,698    $  5,610         --            --

(a) Applicable to common stockholders.

(b) Cash flow includes net loss plus impairment charges, depletion and 
    depreciation.

     CONTACT: Meridian Resource Corporation, Houston
              Joseph A. Reeves Jr., Michael J. Mayell, or
              P. Richard "Dick"Gessinger, 281/558-8080