**BRIGHAM
      EXPLORATION COMPANY**





**1997
      INCENTIVE PLAN**





**RESTRICTED
      STOCK AGREEMENT**





THIS
      AGREEMENT, made as of the 10th day of October, 2005, by and between BRIGHAM
      EXPLORATION COMPANY, a Delaware corporation (the “Company”), and
      __________________ (“Employee”);





**W
      I T N E S S E T H:**





WHEREAS,
      the Compensation Committee of the Board of Directors of the Company (the
“Committee”), acting under the Company’s 1997 Incentive Plan (the “Plan”), has
      determined that it is desirable to award shares of restricted stock to Employee
      under the Plan; and





WHEREAS,
      pursuant to the Plan, the Committee has determined that the shares of restricted
      stock so awarded shall be subject to the restrictions, terms and conditions
      of
      this Agreement;





NOW,
      THEREFORE, in consideration of the premises and mutual covenants and agreements
      herein contained, the receipt and sufficiency of which are hereby acknowledged,
      the parties hereby agree as follows:





1. Plan
      Provisions .
      Capitalized terms used and not otherwise defined herein shall have the
      respective meanings given such terms in the Plan. By execution of this
      Agreement, Employee agrees that the Restricted Stock covered hereby shall be
      governed by and subject to all applicable provisions of the Plan. This Agreement
      is subject to the Plan, and the Plan shall govern where there is any
      inconsistency between the Plan and this Agreement.




2. Restricted
      Stock .
      On the
      terms and conditions and subject to the restrictions, including forfeiture,
      hereinafter set forth, the Company hereby makes to Employee, and Employee hereby
      accepts, the awards of Restricted Stock (each such issuance is herein called
      an
“Award”) set forth on Exhibit
      A hereto,
      which awards are being issued by the Company pursuant to the Plan. The number
      of
      shares of Restricted Stock of each Award covered hereby (the “Restricted
      Shares”), the date of issuance of such shares (the “Issue Date”), and the
      Restricted Period applicable to such shares, including the date on which such
      Restricted Period is scheduled to terminate (the “Scheduled Termination Date”),
      are set forth on Exhibit
      A attached
      hereto. A certificate or certificates representing the Restricted Shares shall
      be issued in the name of Employee as of the applicable Issue Date and delivered
      to Employee on such Issue Date or as soon thereafter as practicable. Employee
      shall cause the certificate(s) representing the Restricted Shares, upon receipt
      thereof by Employee, to be deposited, together with stock powers and any other
      instrument of transfer reasonably requested by the Company duly endorsed in
      blank, with the Company, to be held by the Company in escrow for Employee’s
      benefit until such time as any Restricted Shares represented by such
      certificate(s) are forfeited to the Company or the restrictions thereon
      terminate. Restricted Shares shall be delivered to Employee upon vesting or
      assigned and transferred to and reacquired by the Company upon forfeiture,
      as
      hereinafter set forth.





3. Vesting/Forfeiture .





(a) Subject
      to Sections 3(b), 3(c) and 3(d), with respect to each Award of Restricted Shares
      to Employee, the Restricted Shares subject to such Award shall be forfeited
      to
      the Company at no cost to the Company if Employee’s employment with the Company
      or a subsidiary of the Company terminates prior to the termination of the
      Restricted Period applicable to such Restricted Shares.





(b) Upon
      Employee’s termination of employment during the Restricted Period due to death
      during the Restricted Period, then, the Awards covered hereby that have not
      vested shall be deemed to have vested as of the date of the Employee’s death and
      the Restricted Period applicable to such shares shall terminate.





(c) Upon
      (i)
      Employee’s termination of employment during the Restricted Period due to
      Disability (as defined below), or (ii) the involuntary termination of Employee’s
      employment with the Company and its subsidiaries by action of the Company (or
      its subsidiary, if Employee is employed by a subsidiary of the Company) during
      the Restricted Period for reasons other than Just Cause (as defined below)
      (each, a “Termination Event”), then, with respect to the Award covered hereby
      with the earliest Scheduled Termination Date after such Termination Event,
      (A) a
      ratable portion of the number of Restricted Shares applicable to such Scheduled
      Termination Date (the “Next Vested Shares”) shall be deemed to have vested as of
      the date of such Termination Event, determined by multiplying the number of
      Next
      Vested Shares by a fraction with a numerator equal to the number of full months
      which have then elapsed since the last date of termination of a Restricted
      Period pursuant to this Agreement (or Issue Date in the event that no shares
      had
      previously vested) and a denominator equal to the total number of months between
      the last date of termination of a Restricted Period pursuant to this Agreement
      (or Issue Date in the event that no shares had previously vested) and the next
      Scheduled Termination Date under this Agreement, and rounding to the closest
      whole number, and (B) the Restricted Period applicable to such ratable portion
      of Next Vested Shares shall terminate.





(d) If
      either
      (1) Ben M. Brigham is no longer both the Chief Executive Officer and Chairman
      of
      the Board of the Company, or (2) any
      “person,” as that term is defined in Section 3(a)(9) of the Securities Exchange
      Act of 1934 (the “Exchange Act”) (other than the Company, any of its
      subsidiaries, any employee benefit plan of the Company or any of its
      subsidiaries, or any entity organized, appointed or established by the Company
      for or pursuant to the terms of such a plan), together with all “affiliates” and
“associates” (as such terms are defined in Rule 12b-2 under the Exchange Act) of
      such person, or any “Person” or “group” (as those terms are used in Sections
      13(d) and 14(d) of the Exchange Act), becomes the “beneficial owner” or
“beneficial owners” (as defined in Rules 13d-3 and 13d-5 under the Exchange
      Act), directly or indirectly, of securities of the Company representing in
      the
      aggregate forty-nine percent (49%) or more of either the then outstanding shares
      of Common Stock of the Company or the voting power of the Company, in either
      such case (each of the events described in (1) and (2) above being referred
      to
      herein as a "Fundamental Change"), and Recipient’s employment with the Company
      is involuntarily terminated within two (2) years of such Fundamental Change,
      then immediately upon such termination, the unvested Restricted Shares shall
      be
      forfeited to the Company at no cost to the Company and Employee shall receive
      a
      new separate grant of __________________ (___00) shares of fully vested and
      unrestricted Company common stock


2


(the
      “Additional Grant”). In the event that within two (2) years of a Fundamental
      Change Employee’s job responsibilities are substantially reduced, his annual
      salary is reduced, or he is required to move his office location more than
      30
      miles from its existing location, and Employee terminates his employment due
      to
      such reduction or required move within 15 days of such reduction or the
      announcement of the required move, then Employee shall be deemed to have been
      involuntarily terminated for purposes of this paragraph, and immediately upon
      such termination, the unvested Restricted Shares shall be forfeited to the
      Company at no cost to the Company and Employee shall receive the Additional
      Grant of _____________ (____00) shares. However, notwithstanding the above,
      the
      Company’s obligation to issue the Additional Grant shall be contingent upon the
      Company having availability under the Plan.





(e) Unless
      and until Restricted Shares are delivered to Employee upon vesting, such
      Restricted Shares shall not be sold, assigned, transferred, discounted,
      exchanged, pledged, or otherwise encumbered or disposed of by Employee in any
      manner. Transfer of employment without interruption of service between or among
      the Company and any of its subsidiaries shall not be considered a termination
      of
      employment.





(f) With
      respect to each Award of Restricted Shares to Employee, upon the termination
      of
      the Restricted Period applicable to such shares, the restrictions applicable
      to
      the Restricted Shares that have not theretofore been forfeited shall terminate,
      and as soon as practicable thereafter a stock certificate for the number of
      Restricted Shares with respect to which the restrictions have terminated,
      together with any dividends or other distributions with respect to such shares
      then being held by the Company pursuant to the provisions of this Agreement,
      shall be delivered, free of all such restrictions, to Employee or Employee’s
      beneficiary or estate, as the case may be.





(g) Notwithstanding
      anything contained herein to the contrary, the Committee shall have the right
      to
      cancel all or any portion of any outstanding restrictions prior to the
      termination of such restrictions with respect to any or all of the Restricted
      Shares on such terms and conditions as the Committee may, in writing, deem
      appropriate.





(h) For
      purposes of this Agreement, the following terms shall have the indicated
      meanings:





Disability:
      The “Disability” of Employee shall be deemed to have occurred if, in the good
      faith judgment of the Committee, Employee shall become unable to continue the
      proper performance of Employee’s duties as an employee of the Company or a
      subsidiary thereof on a full-time basis as a result of Employee’s physical or
      mental incapacity.





Just
      Cause: The term “Just Cause” shall mean any of the following: (i) conduct by
      Employee that constitutes willful misconduct or gross negligence in the
      performance of his duties; (ii) conduct by the Employee that constitutes fraud,
      dishonesty, or a criminal act, whether or not with respect to the Company;
      (iii)
      embezzlement of funds or misappropriation of other property by Employee, (iv)
      any act or conduct by Employee that, in the good faith opinion of the Board
      of
      Directors or the President of the Company, is materially detrimental to the
      Company or reflects unfavorably on the Company or the Employee to such an extent
      that the Company’s best interests reasonably require the Employee’s
      discharge.


3





4. Rights
      as Stockholder .
      Upon
      the issuance of a certificate or certificates representing any Restricted Shares
      to Employee, Employee shall become the owner thereof for all purposes and shall
      have all rights as a stockholder, including voting rights and the right to
      receive dividends and distributions, with respect to such Restricted Shares,
      subject to the provisions hereof. If the Company shall pay or declare a dividend
      or make a distribution of any kind, whether due to a reorganization,
      recapitalization or otherwise, with respect to the shares of Common Stock
      constituting Restricted Shares, then the Company shall pay or make such dividend
      or other distribution with respect to such Restricted Shares; provided, however,
      that the cash, stock or other securities and other property constituting such
      dividend or other distribution shall be held by the Company subject to the
      restrictions applicable to any Restricted Shares until such Restricted Shares
      with respect to which such dividend or other distribution was paid or made
      are
      either vested or forfeited. If any Restricted Shares with respect to which
      such
      dividend or distribution was paid or made do not vest but instead are forfeited
      pursuant to the provisions hereof, then Employee shall not be entitled to
      receive such dividend or distribution with respect to such forfeited shares
      and
      such dividend or distribution with respect to such forfeited shares shall
      likewise be forfeited and automatically transferred to and reacquired by the
      Company. If any Restricted Shares with respect to which such dividend or
      distribution was paid or made become vested pursuant to the provisions hereof,
      then Employee shall be entitled to receive such dividend or distribution with
      respect to such vested shares, without interest, and such dividend or
      distribution with respect to such vested shares shall likewise be delivered
      to
      Employee.





5. Withholding
      Taxes .





(a) With
      respect to each Award of shares of Restricted Stock to Employee, Employee may
      elect, within 30 days of the Issue Date of such shares and on notice to the
      Company, to realize income for federal income tax purposes equal to the fair
      market value of the shares on the Issue Date. In such event, Employee shall
      make
      arrangements satisfactory to the Compensation Committee to pay in the year
      of
      the Award any federal, state, or local taxes required to be withheld with
      respect to such shares. If Employee fails to make such payments, then any
      provision of this Agreement to the contrary notwithstanding, the Company and
      its
      subsidiaries shall, to the extent permitted by law, have the right to deduct
      from any payments of any kind otherwise due from the Company or its subsidiaries
      to or with respect to Employee, whether or not pursuant to this Agreement or
      the
      Plan and regardless of the form of payment, any federal, state, or local taxes
      of any kind required by law to be withheld with respect to such shares.





(b) (i) No
      later
      than the date of the termination of the restrictions on any of the shares of
      Restricted Stock covered hereby, Employee will pay to the Company or its
      subsidiaries, or make arrangements satisfactory to the Compensation Committee
      regarding payment of, any statutory minimum taxes required by law to be withheld
      with respect to the shares of Restricted Stock with respect to which such
      restrictions have terminated.




(ii) The
      Company may elect to allow Employee, to the extent permitted by law, to deliver
      to the Company or its subsidiaries shares of Restricted Stock to which Employee
      shall be entitled upon the vesting thereof (or other unrestricted shares of
      Common Stock owned by Employee), valued at the fair market value of such shares
      at the time of such delivery to the Company or its subsidiaries, to satisfy
      the
      obligation of Employee under Section 5(b)(i) hereof.


4





(iii) Any
      provision of this Agreement to the contrary notwithstanding, if Employee does
      not otherwise satisfy the obligation of Employee under Section 5(b)(i) hereof,
      then the Company and its subsidiaries shall, to the extent permitted by law,
      have the right to deduct from any payments of any kind otherwise due from the
      Company or its subsidiaries to or with respect to Employee, whether or not
      pursuant to this Agreement or the Plan and regardless of the form of payment,
      any federal, state, or local taxes of any kind required by law to be withheld
      with respect to the shares of Restricted Stock with respect to which the
      restrictions on the Restricted Stock have terminated.





6. Legend .
      Each
      certificate representing shares of Restricted Stock covered hereby shall
      conspicuously set forth on the face or back thereof, in addition to any legends
      required by applicable law or other agreement, a legend in substantially the
      following form:





THE
      SHARES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ASSIGNED AND TRANSFERRED TO
      THE
      RECORD HOLDER HEREOF PURSUANT TO THE TERMS OF THE BRIGHAM EXPLORATION COMPANY
      1997 INCENTIVE PLAN AND MAY NOT BE SOLD, ASSIGNED, TRANSFERRED, DISCOUNTED,
      EXCHANGED, PLEDGED, OR OTHERWISE ENCUMBERED OR DISPOSED OF IN ANY MANNER EXCEPT
      AS SET FORTH IN THE TERMS OF THE AGREEMENT EMBODYING THE AWARD OF SUCH SHARES
      DATED OCTOBER 10, 2005. A COPY OF SUCH PLAN AND AGREEMENT IS ON FILE IN THE
      OFFICES OF THE CORPORATION.





7. Governing
      Law .
      This
      Agreement shall be governed by and construed and enforced in accordance with
      the
      laws of the State of Delaware, without regard to the principles of conflicts
      of
      laws thereof.





8. Binding
      Effect .
      This
      Agreement shall be binding upon and inure to the benefit of the parties hereto
      and their respective heirs, personal representatives, successors, and permitted
      assigns; provided, however, that Employee shall not assign or otherwise transfer
      this Agreement or any of Employee’s rights or obligations
      hereunder.





9. Entire
      Agreement; Amendment .
      This
      Agreement, together with the exhibits hereto and any other writings referred
      to
      herein or delivered pursuant hereto, constitute the entire agreement between
      the
      parties hereto with respect to the subject matter hereof and supersede all
      prior
      agreements and understandings, whether written or oral, between the parties
      with
      respect to the subject matter hereof. To the fullest extent provided by
      applicable law, this Agreement may be amended, modified, and supplemented by
      mutual consent of the parties hereto at any time, with respect to any of the
      terms contained herein, in such manner as may be agreed upon in writing by
      such
      parties.





10. Notices .
      All
      notices and other communications hereunder shall be in writing and shall be
      deemed given:





(a) If
      to the
      Company, when delivered by hand or on the third business day after being
      deposited in the United States mail (certified mail with postage prepaid)
      to:




5




Brigham
        Exploration Company
 6300
        Bridge Point Parkway


Building
      2, Suite 500


Austin,
      Texas 78730


Attention:
      Vice President Administration





(b) If
      to
      Employee, when delivered by hand or on the third business day after being
      deposited in the United States mail (certified mail with postage prepaid) to
      the
      address for Employee contained in the Company’s records.





Either
      party may at any time give to the other notice in writing of any change of
      address of the party giving such notice and from and after the giving of such
      notice the address or addresses therein specified will be deemed to be the
      address of such party for the purposes of giving notice hereunder.





11. Counterparts .
      This
      Agreement may be executed by the parties hereto in any number of counterparts,
      each of which shall be deemed an original, but all of which shall constitute
      one
      and the same agreement. Each counterpart may consist of a number of copies
      hereof each signed by less than all, but together signed by all, the parties
      hereto.




IN
      WITNESS WHEREOF, the Company and Employee have executed this Agreement as of
      the
      date first above written.





BRIGHAM
                EXPLORATION COMPANYBy:Name: 
                Ben M. BrighamTitle: 
                President and CEO




6





EXHIBIT
      A





**RESTRICTED
      STOCK AWARDS**





Award
            
            Number
                of
              Shares
                ofRestrictedStock
            
            Issue
                Date
            
            Duration
                of
              Restricted
                Period
            
            Scheduled
              Termination
                Date1.
            
            ____
            
            October
                10, 2005
            
            Commencing
                on October 10, 2005 and ending at 12:01 AM on October 10,
                2006
            
            12:01
                AM on October 10, 20062.
            
            ____
            
            October
                10, 2005
            
            Commencing
                on October 10, 2005 and ending at 12:01 AM on October 10,
                2007
            
            12:01
                AM on October 10, 20073.
            
            ____
            
            October
                10, 2005
            
            Commencing
                on October 10, 2005 and ending at 12:01 AM on October 10,
                2008
            
            12:01
                AM on October 10, 20084.
            
            ____
            
            October
                10, 2005
            
            Commencing
                on October 10, 2005 and ending at 12:01 AM on October 10,
                2009
            
            12:01
                AM on October 10, 20095.
            
            ____
            
            October
                10, 2005
            
            Commencing
                on October 10, 2005 and ending at 12:01 AM on October 10,
                2010
            
            12:01
                AM on October 10, 2010




7