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**Exhibit      31.2**

**CERTIFICATION          OF CHIEF FINANCIAL OFFICER**

**PURSUANT          TO RULE 13a-14(a) OF THE **

**SECURITIES          EXCHANGE ACT OF 1934**

| 1. | I                    have reviewed this quarterly report on Form 10-Q of Brigham                    Exploration Company; |
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| 2. | Based                    on my knowledge, this annual report does not contain any untrue                    statement                    of a material fact or omit to state a material fact necessary                    to make the                    statements made, in light of the circumstances under which such                    statements                    were made, not misleading with respect to the period covered                    by this                    annual report; |
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| 3. | Based                    on my knowledge, the financial statements, and other financial                    information                    included in this annual report, fairly present in all material                    respects                    the financial condition, results of operations and cash flows                    of the                    registrant as of, and for, the periods presented in this annual                    report; |
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| 4. | The                    registrant's other certifying officer and I are responsible for                    establishing and maintaining disclosure controls and procedures                    (as                    defined in Exchange Act Rules 13a-15(e) and 15d-15(e))                    and internal                    control over financial reporting (as defined in Exchange Act                    Rules                    13a-15(f) and 15d-15(f)) for the registrant and                    have: |
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|   | a) | Designed                    such disclosure controls and procedures or caused such disclosure                    controls                    and procedures to be designed under our supervision, to ensure                    that                    material information relating to the registrant, including its                    consolidated subsidiaries, is made known to us by others within                    those                    entities, particularly during the period in which this report                    is being                    prepared; |
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|   | b) | Designed                    such internal control over financial reporting, or caused such                    internal                    control over financial reporting to be designed under our supervision,                    to                    provide reasonable assurance regarding the reliability of financial                    reporting and the preparation of financial statements for external                    purposes in accordance with generally accepted accounting                    principles; |
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|   | c) | Evaluated                    the effectiveness of the registrant's disclosure controls and                    procedures                    and presented in this report our conclusions and about the effectiveness                    of the disclosure controls and procedures, as of the end of the                    period                    covered by this report based on such evaluation;                    and |
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|   | d) | Disclosed                    in this report any change in the registrant’s internal control over                    financial 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 has materially affected, or is reasonably                    likely to                    materially affect, the registrant’s internal control over financial                    reporting; and |
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| 5. | The                    registrant's other certifying officer and I have disclosed, based                    on our                    most recent evaluation of internal control over financial reporting,                    to                    the registrant's auditors and the audit committee of registrant's                    board of                    directors (or persons performing the equivalent                    function): |
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|   | a) | All                    significant deficiencies and material weaknesses in the design                    or                    operation of internal control over financial reporting, which                    are                    reasonably likely to adversely affect the registrant's ability                    to record,                    process, summarize and report financial information;                    and |
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|   | b) | Any                    fraud, whether or not material, that involves management or other                    employees who have a significant role in the registrant's internal                    control                    over financial reporting. |
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|   | /s/                EUGENE                B.                SHEPHERD,                JR. |   |
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|   | Eugene                B. Shepherd, Jr.                                                  |   |
|   | Executive                Vice President and Chief Financial Officer                     |   |

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