Exhibit 99.2

                           CERTIFICATE OF ELIMINATION

                                       OF

             CERTIFICATE OF DESIGNATIONS OF SERIES B PREFERRED STOCK

                                       OF

                           BRIGHAM EXPLORATION COMPANY

     Brigham Exploration Company (the "Company"), a corporation organized and
existing under the General Corporation Law of the State of Delaware (the "DGCL")
does hereby certify that:

     1.     The Certificate of Incorporation of the Company was filed in the
office of the Secretary of State of Delaware on February 25, 1997 and a
Certificate of Designations of Series B Preferred Stock (the "Certificate of
Designations") was filed in the office of the Secretary of State on December 20,
2002.

     2.     By unanimous written consent, the Board of Directors of the Company
adopted the resolutions attached as Exhibit A authorizing the elimination of the
                                    ---------
Certificate of Designations from the Company's Certificate of Incorporation in
accordance with the provisions of Section 151 of the DGCL.

     IN WITNESS WHEREOF, the Company has caused this Certificate of Cancellation
of Certificate of Designations of Series B Preferred Stock to be signed by its
duly authorized officer on June 4, 2004.

                                      BRIGHAM  EXPLORATION  COMPANY



                                      By:  /s/  Ben M. Brigham
                                           ------------------------------
                                                Ben M. Brigham, Chief Executive
                                                Officer  and  President



                                    EXHIBIT A
                                    ---------

RELATING TO SERIES B PREFERRED STOCK

     WHEREAS, there are no shares of Series B Preferred Stock issued and no
shares of Series B Preferred Stock will be issued in the future;

     NOW, THEREFORE, BE IT RESOLVED, that the Board of Directors deems it in the
best interest of the Company to eliminate the Certificate of Designations of
Series B Preferred Stock from the Company's Certificate of Incorporation
pursuant to Section 151(g) of the General Corporation Law of the State of
Delaware;

     RESOLVED FURTHER, that the President, any Vice President and the Corporate
Secretary of the Company, and each of them, are hereby authorized to execute a
Certificate of Cancellation of the Certificate of Designations of Series B
Preferred Stock and to file the Certificate of Cancellation with the Secretary
of State of Delaware.

RELATING TO FURTHER AUTHORIZATION

     RESOLVED FURTHER, that the proper officers of the Company are hereby
authorized to execute, deliver and file any other instruments and documents and
to take any other actions as they may deem necessary or advisable to accomplish
the purpose of the foregoing resolutions.

     RESOLVED FURTHER, that all actions heretofore taken by the officers of the
Company with respect to the matters covered by the foregoing resolutions are
hereby ratified, confirmed and approved in all respects.