================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 ---------------

                                    FORM 8-K

                                 CURRENT REPORT

     Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

                                 ---------------

         Date of Report (Date of earliest event reported): March 4, 2004

                           BRIGHAM EXPLORATION COMPANY
             (Exact name of registrant as specified in its charter)

          Delaware                     000-22433                 75-2692967
(State or other jurisdiction          (Commission              (IRS Employer
      of incorporation)               File Number)           Identification No.)

                            6300 Bridgepoint Parkway
                             Building Two, Suite 500
                               Austin, Texas 78730
          (Address, including zip code, of principal executive offices)

       Registrant's telephone number, including area code: (512) 427-3300

================================================================================


Item 7. Financial Statements and Exhibits.

      (c)   Exhibit 99.1 Press release dated March 4, 2004.

Item 12. Regulation FD Disclosure.

      Registrant is furnishing its press release dated March 4, 2004, which
announces the Registrant's financial results for the quarter ended December 31,
2003 and the twelve month period ended December 31, 2003 and provides its first
quarter 2004 forecast. The text of the press release is furnished as attached
hereto as Exhibit 99.1.

                                    SIGNATURE

      Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                                  BRIGHAM EXPLORATION COMPANY

Date: March 5, 2004
                                                  By: /s/ Eugene B. Shepherd, Jr
                                                      --------------------------
                                                      Eugene B. Shepherd, Jr.
                                                      --------------------------
                                                      Executive Vice President &
                                                      Chief Financial Officer


                                INDEX TO EXHIBITS

            Item Number                    Exhibit
            -----------                    -------

            99.1*             Press Release dated March 4, 2004