Exhibit 99.1

 Brigham Exploration Reports Record First Quarter 2004 Production and Financial
                                    Results

    AUSTIN, Texas, May 10 /PRNewswire-FirstCall/ -- Brigham Exploration
Company (Nasdaq: BEXP) today announced its financial results for the quarter
ended March 31, 2004.

     Highlights from Brigham's performance for the first quarter include:
     --  First quarter 2004 production of 33.9 MMcfe/d, representing a 9%
         increase over first quarter 2003 production and a 15% sequential
         increase over fourth quarter 2003 production;
     --  15% increase in revenues to $16.8 million, compared to revenues in
         last year's first quarter of $14.7 million;
     --  11% increase in operating income to $8.2 million, compared to
         operating income in last year's first quarter of $7.4 million; and
     --  111% increase in net capital expenditures to $17 million, relative to
         net capital expenditures in last year's first quarter of $8 million.
    FIRST QUARTER 2004 RESULTS
    Average daily production volumes for the first quarter 2004 were
33.9 MMcfe/d and were 9% higher when compared with production volumes in last
year's first quarter and 15% higher than production volumes in the fourth
quarter 2003.  Revenue from the sale of oil and natural gas for the first
quarter increased 15% despite a 10% decrease in our pre-hedge sales price.
Increased production volumes resulted in a $2.4 million increase in revenues,
and a decline in losses on the settlement of derivative contracts resulted in
an additional $2.6 increase in revenues.  These increases were partially
offset by a $2.8 million decrease in revenues due to lower commodity prices.
    An increase in workover activity, ad valorem taxes and the number of
producing wells in the first quarter 2004 led to a 45% increase in lease
operating expenses.  Lease operating expenses, on a per unit basis, for the
first quarter 2004 increased $0.11 per Mcfe to $0.46.  Increases in compressor
rental and maintenance expense and fees paid for overhead represented
approximately $0.03 per Mcfe of the increase, while the increase in workover
costs and ad valorem taxes represented $0.08 of the increase.  A decrease in
the average pre-hedge sales price that we received for oil and natural gas in
the first quarter 2004 resulted in an 8% decline in our total production tax
expense and $0.05 per Mcfe decline on a per unit basis.
    General and administrative expenses for the first quarter 2004 were up 7%
when compared to general and administrative expenses for the first quarter
last year.  A decrease in the percentage of our total general and
administrative costs that we capitalized in the first quarter 2004 and an
increase in employee compensation expenses, corporate insurance costs and
franchise taxes were the primary reasons for the increase in general and
administrative expenses.  General and administrative expenses on a per unit
basis decreased 2% in the first quarter 2004 to $0.40 per Mcfe.
    Depletion expense for the first quarter 2004 was $4.9 million ($1.60 per
Mcfe) compared to $4.1 million ($1.46 per Mcfe) in the first quarter last
year.  An increase in our depletion rate accounted for 55% of this increase
while an increase in production accounted for 45% of the increase.  Operating
income for the first quarter 2004 was $8.2 million and grew 11% when compared
to operating income in the first quarter last year.
    A decline in our weighted average debt balances outstanding under both our
senior credit facility and our senior subordinated notes, combined with a
decrease in the interest rate that we paid on those borrowings, were the
primary reasons for the $500,000 or 39% decrease in interest expenses for the
first quarter 2004.  Interest expenses for the first quarter 2004 were
$782,000 and $0.26 per Mcfe on a per unit basis, compared to $1.3 million and
$0.46 in 2003.
    We reported net income available to common stockholders of $5.1 million
($0.13 per diluted share) in the first quarter 2004 versus a net income of
$5.5 million ($0.20 per diluted share) for the prior year period.  Net income
in the current quarter was reduced by a $2.5 million provision for deferred
income taxes.  There was no income tax provision incurred in last year's first
quarter.
    Our capital expenditures for the first quarter 2004 increased 111%.  Net
capital expenditures for the first quarter of 2004 and 2003 were:

                                          ($'s in millions)
                                     Three Months Ended March 31,
                                         2004            2003
     Drilling                            $12.6            $5.2
     Net land and G&G                      2.8             1.3
     Capitalized costs                     1.6             1.7
     Proceeds from the sale of assets     (0.0)           (0.2)
       Net capital expenditures          $17.0            $8.0

    SECOND QUARTER 2004 FORECAST
    The following forecasts and estimates of our second quarter 2004 results
are forward looking statements subject to the risks and uncertainties
identified in the "Forward Looking Statements Disclosure" at the end of this
release.
    We currently expect second quarter 2004 production volumes to average
between 34 and 36 MMcfe/d (70% natural gas).  For the second quarter 2004,
lease operating expenses are projected to be $0.45 per Mcfe, production taxes
are projected to be approximately 5.5% of pre-hedge oil and natural gas
revenues, and general and administrative expenses are projected to be
$1.2 million ($0.37 to $0.39 per Mcfe).
    Based on these production and cost estimates, assumed average NYMEX prices
of $5.80 per MMBtu for natural gas and $38.00 per barrel for oil, and taking
into account current derivative contracts outstanding, we forecast that our
revenue will be between $16.9 and $18 million and operating income will be
between $8.2 and $8.9 million for the second quarter 2004.
    Gene Shepherd, Brigham's Chief Financial Officer, commented, "We are very
pleased with our first quarter operating performance.  Revenues and operating
income were all up substantially, due to the strong production growth that
resulted from the acceleration in our drilling activity beginning in late 2003
and the continued strong commodity prices.  Going forward, we expect continued
growth in our production volumes, driven by the 74% increase in our year-over-
year drilling budget.  Combining this anticipated production growth with
strong commodity prices should generate substantial value appreciation for our
shareholders over the coming quarters."
    Shepherd further added, "Given high commodity prices and our improved
revenue realizations, our operating profit per Mcfe expanded to $4.37,
relative to $3.69 in 2003 and $2.45 in 2002.  We believe that this illustrates
the opportunity we are seizing to compound value for our shareholders through
our accelerated drilling program in this window of high commodity prices."

    CONFERENCE CALL INFORMATION
    Our management will host a conference call to discuss its operational and
financial results for the first quarter 2004 with investors, analysts and
other interested parties on Tuesday, May 11th, at 9:00 a.m. Central time.  To
participate in the call, participants within the U.S. please dial 800-299-8538
and participants outside the U.S. please dial 617-786 -2902.  The participant
passcode for the call is 99234703.  A telephone recording of the conference
call will be available to interested parties approximately two hours after the
call is completed through 11:59 p.m. Central time on Tuesday, May 25th.  To
access the recording, domestic callers dial 888-286-8010 and international
callers dial 617-801-6888.  The passcode for the conference call playback is
35674419.  In addition, a live and archived web cast of the conference call
will be available over the Internet at either www.bexp3d.com or
www.streetevents.com .  A copy of this press release and other financial and
statistical information about the periods covered by this press release and by
the conference call that will take place on May 11, 2004, will be available on
our website.  To access the press release go to www.bexp3d.com and click on
News Releases.  The file with a copy of the press release is named Brigham
Exploration Reports Record First Quarter 2004 Production and Financial Results
and is dated May 10, 2004.  To access the other financial and statistical
information that will be covered by the conference call that will take place
on May 11, 2004, go to www.bexp3d.com and click on Event Calendar.  The file
with the other financial and statistical information is named Financial and
Statistical Information for the First Quarter Conference Call and is dated
May 11, 2004.

    ABOUT BRIGHAM EXPLORATION
    Brigham Exploration Company is an independent exploration and production
company that applies 3-D seismic imaging and other advanced technologies to
systematically explore and develop onshore domestic natural gas and oil
provinces.  For more information about Brigham Exploration, please visit our
website at www.bexp3d.com or contact Investor Relations at 512-427-3444.

    FORWARD LOOKING STATEMENTS DISCLOSURE
    Except for the historical information contained herein, the matters
discussed in this news release are forward looking statements within the
meaning of the Private Securities Litigation Reform Act of 1995 that are based
upon current expectations.  Important factors that could cause actual results
to differ materially from those in the forward looking statements include
risks inherent in exploratory drilling activities, the timing and extent of
changes in commodity prices, unforeseen engineering and mechanical or
technological difficulties in drilling wells, availability of drilling rigs,
land issues, federal and state regulatory developments and other risks more
fully described in the company's filings with the Securities and Exchange
Commission.  All forward looking statements contained in this release,
including any forecasts and estimates, are based on management's outlook only
as of the date of this release, and we undertake no obligation to update or
revise these forward looking statements, whether as a result of subsequent
developments or otherwise.

     Contact:  John Turner, Manager - Finance & Investor Relations
               (512) 427-3300 / investor@bexp3d.com

                         BRIGHAM EXPLORATION COMPANY
                SUMMARY CONSOLIDATED STATEMENTS OF OPERATIONS
              (in thousands, except per share data) (unaudited)
                                                 Three Months Ended March 31,
                                                      2004           2003
    Revenues:
      Oil and natural gas sales                      $16,819        $14,639
      Other                                                1             38
                                                     $16,820        $14,677
      Costs and expenses:
      Lease operating                                  1,409            974
      Production taxes                                   863            938
      General and administrative                       1,220          1,139
      Depletion of natural gas and oil properties      4,880          4,102
      Depreciation and amortization                      181             97
      Accretion of asset retirement obligation            37             34
                                                      $8,590         $7,284
        Operating income                              $8,230         $7,393
    Interest expense                                    (782)        (1,282)
    Interest income                                       14             21
    Other income (expense) (A)                           127            111
        Income (loss) before income taxes and
         accounting change                            $7,589         $6,243
    Income tax benefit (expense)                      (2,500)           ---
        Net income (loss) before accounting change    $5,089         $6,243
    Cumulative effect of adoption of accounting
     principle                                           ---            268
      Net income (loss)                               $5,089         $6,511
    Preferred stock dividend & accretion                 ---            995
        Net income (loss) to common                   $5,089         $5,516
    Net income (loss) to common per share:
      Basic                                            $0.13          $0.28
      Diluted                                           0.13           0.20
    Wt. avg. common shares outstanding:
      Basic                                           39,166         19,707
      Diluted                                         40,211         32,111
     (A)  Includes non-cash gain (loss) related
           to changes in the fair market value of
           our derivative contracts of:                 $127           $111

                         BRIGHAM EXPLORATION COMPANY
              PRODUCTION, SALES PRICES AND OTHER FINANCIAL DATA
                                 (unaudited)
                                                 Three Months Ended March 31,
                                                       2004           2003
    Average net daily production:
      Natural gas (MMcf)                                23.3           16.4
      Oil (Bbls)                                       1,773          2,475
        Equivalent natural gas (MMcfe) (6:1)            33.9           31.2
    Total net production:
      Natural gas (MMcf)                               2,093          1,472
      Oil (MBbls)                                        160            223
        Equivalent natural gas (MMcfe) (6:1)           3,050          2,808
        % Natural gas                                    69%            52%
    Sales prices (Before hedging):
      Natural gas ($/Mcf)                              $5.79          $7.23
      Oil ($/Bbl)                                      34.01          32.88
        Equivalent natural gas (MMcfe) (6:1)            5.75           6.40
    Realized prices (Post hedging):
      Natural gas ($/Mcf) (A)                          $5.69          $5.53
      Oil ($/Bbl) (A)                                  30.84          29.16
        Equivalent natural gas (MMcfe) (6:1)            5.51           5.21
     (A)  Includes the effects of hedging gains
           (losses) of:
          Natural gas ($/Mcf)                         $(0.10)        $(1.70)
          Oil ($/Bbl)                                  (3.17)         (3.72)

                     SUMMARY CONSOLIDATED BALANCE SHEETS
                          (in thousands) (unaudited)
                                                  03/31/2004     12/31/2003
    Assets:
      Current assets                                 $22,376        $20,835
      Oil and gas properties, at cost, net           209,503        197,311
      Other property and equipment, at cost, net       1,251          1,219
      Other non-current assets                         2,771          4,851
        Total assets                                $235,901       $224,216
    Liabilities and stockholders' equity:
      Current liabilities                            $31,996        $35,579
      Notes payable                                   29,200         19,000
      Senior subordinated notes                       20,000         20,000
      Series A Preferred Stock, mandatorily
       redeemable                                      8,969          8,794
      Other non-current liabilities                    2,923          2,498
        Total liabilities                            $93,088        $85,871
      Stockholders' equity                           142,813        138,345
        Total liabilities and stockholders' equity  $235,901       $224,216

                         BRIGHAM EXPLORATION COMPANY
                SUMMARY CONSOLIDATED STATEMENTS OF CASH FLOWS
                          (in thousands) (unaudited)
                                                 Three Months Ended March 31,
                                                      2004           2003
    Cash flows from operating activities:
      Net income (loss)                               $5,089         $6,511
      Depletion, depreciation and amortization         5,061          4,199
      Accretion of asset retirement obligation            37             34
      Interest paid through issuance of add'l
       senior sub. notes                                 ---            296
      Amortization of deferred loan fees and debt
       issuance cost                                     192            253
      Interest paid through issuance of add'l
       redeemable preferred stock                        175            ---
      Market value adjustments for derivatives          (127)          (111)
      Deferred income tax (benefit) expense            2,500            ---
      Cumulative effect of adoption of
       accounting principle                              ---           (268)
      Changes in assets and liabilities               (4,333)         4,148
        Net cash provided by operating activities     $8,594        $15,062
        Net cash used by investing activities        (17,057)        (9,339)
        Net cash provided (used) by financing
         activities                                   10,343         (4,556)
        Net increase (decrease) in cash and
         cash equivalents                             $1,880         $1,167

                            SUMMARY PER MCFE DATA
                                 (unaudited)
                                                 Three Months Ended March 31,
                                                       2004           2003
    Revenues:
      Oil and natural gas sales                        $5.51          $5.21
      Other                                             0.00           0.01
                                                       $5.51          $5.22
    Costs and expenses:
      Lease operating                                   0.46           0.35
      Production taxes                                  0.28           0.33
      General and administrative                        0.40           0.41
      Depletion of natural gas and oil properties       1.60           1.46
      Depreciation and amortization                     0.06           0.03
      Accretion of asset retirement obligation          0.01           0.01
                                                       $2.81          $2.59
        Operating income                               $2.70          $2.63
      Interest expense, net of interest income         (0.25)         (0.45)
      Other income (expense) (A)                        0.00           0.00
        Net income before preferred stock
         dividend & accretion                          $2.45          $2.18
     (A)  Adjusted to exclude non-cash income (expense) related to changes in
          the fair market value of our derivative contracts.

                         BRIGHAM EXPLORATION COMPANY
       SUMMARY OF COMMODITY PRICE HEDGES OUTSTANDING AS OF MAY 10, 2004
                                 (unaudited)
                                    2004                      2005
                             Q2      Q3      Q4       Q1      Q2    Q3   Q4
    Natural
     Gas Swaps: MMBtu/d    2,500   1,500   1,000      ---     ---   ---  ---
                $/MMBtu   $4.252  $4.180  $4.360      ---     ---   ---  ---
    Natural Gas
     Collars:   Floor -
                 MMBtu/d   5,600   7,850   6,371    5,750   5,000   ---  ---
                Floor -
                 $/Mmbtu  $4.112  $4.613  $4.746   $4.663  $4.725   ---  ---
                Cap -
                 MMBtu/d   5,600   7,850   6,371    5,750   5,000   ---  ---
                Cap -
                 $/MMBtu  $5.672  $6.476  $6.690   $7.100  $6.712   ---  ---
    Crude Oil
     Swaps:     Bbls/d       225     150     100      ---     ---   ---  ---
                $/Bbl     $24.52  $23.91  $23.80      ---     ---   ---  ---
    Crude Oil
     Collars:   Floor -
                 Bbls/d      550     530     372      305     205   ---  ---
                Floor -
                 $/Bbl    $24.09  $26.34  $26.68   $25.56  $26.80   ---  ---
                Cap -
                 Bbls/d      550     530     372      305     205   ---  ---
                Cap -
                 $/Bbl    $30.60  $32.20  $31.71   $30.18  $32.51   ---  ---

    Note: Hedged volumes and prices reflected in this table represent average
contract amounts for the quarterly periods presented; natural gas hedge prices
and crude oil hedge contract prices are based on NYMEX pricing.

SOURCE  Brigham Exploration Company
    -0-                             05/10/2004
    /CONTACT:  John Turner, Manager - Finance & Investor Relations of Brigham
Exploration Company, +1-512-427-3300, or investor@bexp3d.com /
    /Web site:  http://www.streetevents.com /
    /Web site:  http://www.bexp3d.com /
    (BEXP)

CO:  Brigham Exploration Company
ST:  Texas, Oklahoma
IN:  OIL
SU:  ERN CCA MAV ERP