1
 
                                                                    EXHIBIT 23.1
 
                       CONSENT OF INDEPENDENT ACCOUNTANTS
 
     We hereby consent to the incorporation by reference in the Registration
Statement on Form S-8 (No. 333-56961) of Brigham Exploration Company and in the
Registration Statement on Form S-8 (No. 333-70137) of Brigham Exploration
Company of our report dated March 6, 1998, except as to Note 11 which is as of
February 27, 1999, which appears on page F-15 of this Form 10-K/A of Brigham
Exploration Company.
 
                                            PRICEWATERHOUSECOOPERS LLP
 
Houston, Texas
February 27, 1999