**EXHIBIT 31.1**
**CERTIFICATION**
     I, Bud M. Brigham, certify that:
1.  I have reviewed this annual report on Form 10-K of Brigham Exploration Company; 2.  Based on my knowledge, this annual report does not contain any untrue statement of a materialfact or omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this annual report; 3.  Based on my knowledge, the financial statements, and other financial information included inthis annual report, fairly present in all material respects the financial condition, resultsof operations and cash flows of the registrant as of, and for, the periods presented in thisannual report; 4.  The registrant’s other certifying officer and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and we have:
 a)  Designed such disclosure controls and procedures or caused such disclosurecontrols and procedures to be designed under our supervision, to ensure that materialinformation relating to the registrant, including its consolidated subsidiaries, ismade known to us by others within those entities, particularly during the period inwhich this report is being prepared;  b)  Designed such internal control over financial reporting, or caused suchinternal control over financial reporting to be designed under our supervision, toprovide reasonable assurance regarding the reliability of financial reporting and thepreparation of financial statements for external purposes in accordance with generallyaccepted accounting principles;  c)  Evaluated the effectiveness of the registrant’s disclosure controls andprocedures and presented in this report our conclusions and about the effectiveness ofthe disclosure controls and procedures, as of the end of the period covered by thisreport based on such evaluation; and  d)  Disclosed in this report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s most recent fiscal quarter(the registrant’s fourth fiscal quarter in the case of an annual report) that hasmaterially affected, or is reasonably likely to materially affect, the registrant’sinternal control over financial reporting; and
5.  The registrant’s other certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors andthe audit committee of registrant’s board of directors (or persons performing the equivalentfunction):
 a)  All significant deficiencies and material weaknesses in the design or operationof internal control over financial reporting, which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and report financialinformation; and  b)  Any fraud, whether or not material, that involves management or other employeeswho have a significant role in the registrant’s internal control over financialreporting.          Date: March 31, 2005   /s/            Bud M. Brigham Bud M.            Brigham Chief            Executive Officer, President and Chairman            of the Board