AMENDMENT TO
BRIGHAM EXPLORATION COMPANY
1997 DIRECTOR STOCK OPTION PLAN

This Amendment to Brigham Exploration Company 1997 Director Stock Option Plan
(the “Amendment”) is made effective upon approval by the Stockholders of Brigham
Exploration Company (the “Company”) at the 2011 Annual Meeting of Stockholders
to be held June 21, 2011, by the Company for the purpose of amending the Brigham
Exploration Company 1997 Director Stock Option Plan as amended effective
January 1, 2009 (the “Plan”).

RECITALS:

WHEREAS, the Plan provides a seven-year Option Period; and

WHEREAS, the Company now desires to provide a ten-year Option Period;

NOW, THEREFORE, pursuant to the authority reserved in Section 6.02, the Plan is
amended as follows:

AGREEMENT:

1. Section 4.01(d) of the Plan is hereby amended by restatement in its entirety
to read as follows:

(d) Option Period. Each Option shall become exercisable in five equal annual
installments on each of the first five anniversaries of such Option’s “Grant
Date.” The period within which each Option may be exercised shall expire on the
seventh anniversary of such Grant Date (the “Option Period”), unless terminated
sooner pursuant to Section 4.02(e) hereof. Notwithstanding the previous
sentence, for Options granted after June 21, 2011, the period within which each
Option may be exercised shall expire on the tenth anniversary of such Grant Date
(the “Option Period”), unless terminated sooner pursuant to Section 4.02(e)
hereof.

2. Capitalized terms used and not otherwise defined herein have the respective
meanings given to them in the Plan.

IN WITNESS WHEREOF, the undersigned President and Chief Executive Officer has
executed this Amendment as of this 21st day of June, 2011.

BRIGHAM EXPLORATION COMPANY

By: /s/ Ben M. Brigham                        
Name: Ben M. Brigham
Title: President and Chief Executive Officer