Exhibit 3.1

Amendment No. 2
TO THE
SECOND AMENDED AND RESTATED BYLAWS
OF DAWSON GEOPHYSICAL COMPANY

     The Second Amended and Restated Bylaws, as amended (the “Bylaws”) of Dawson Geophysical Company, a Texas corporation (the “Corporation”), are hereby amended as of March 20, 2011, as follows:

1.

Article II, Section 5 of the Bylaws is hereby amended in its entirety and replaced with the following:

     Section 5. Special Meetings. Special meetings of shareholders (i) may be called by the Board of Directors, the Chairman of the Board, the Chief Executive Officer or the President of the Corporation or (ii) shall be called by the President or the Secretary of the Corporation on the written request of the holders of not less than the minimum percentage of shares of the Corporation entitled to vote at the proposed special meeting that is specified by the Corporation’s Articles of Incorporation as necessary to call a special meeting of shareholders (or in the absence of such specification, the minimum percentage necessary to call a special meeting specified by the Texas Business Organizations Code, as amended). Any such request by shareholders shall state the purpose or purposes of the proposed special meeting and the matters proposed to be acted on at that meeting, and shall state, with respect to each requesting shareholder, (i) the name and address, as they appear on the Corporation’s books and records, of the shareholder proposing the special meeting, (ii) evidence reasonably satisfactory to the Secretary of the Corporation, of such shareholder’s status as such and of the number of shares of each class of capital stock of the Corporation of which such shareholder is the beneficial owner, (iii) a description of all arrangements or understandings between such shareholder and any other person or persons (including their names) in connection with the proposal of such special meeting by such shareholder and any material interest of such shareholder in the business to be considered at the special meeting and (iv) a representation that such shareholder intends to appear in person or by proxy at the special meeting. No business shall be conducted at a special meeting except in accordance with the procedures set forth in this Section 5. Beneficial ownership shall be determined in accordance with Rule 13d-3 under the Exchange Act.

          Within 30 days after such shareholder or shareholders shall have submitted the aforesaid items, the Secretary or the Board of Directors of the Corporation shall determine whether the request for a special meeting has been properly submitted and shall notify such shareholder or shareholders in writing of its determination. If such shareholder or shareholders fail to submit a request that satisfies the requirements of this Section 5, or if the Secretary or the Board of Directors of the Corporation determines that the request otherwise has not been properly submitted, then no special meeting shall be called.

          Any requesting shareholder or shareholders may revoke their request for a special meeting at any time by written revocation delivered to the Secretary of the Corporation. In addition, any shareholder request pursuant to this Section 5 of Article II that includes the nomination of a person for the election of directors shall also comply with the provisions of Section 13 of this Article II.

2.

Article II, Section 6 of the Bylaws is hereby amended in its entirety and replaced with the following:

     Section 6. Shareholders of Record and Fixing of Special Meeting Date. Upon receipt of a request for a special meeting of shareholders that is delivered and determined to be valid, in each case, in accordance with Section 5 of this Article II, the Board of Directors shall set a date for the special meeting, set a record date in accordance with Section 10 of this Article II and shall cause the appropriate officer or officers of the Corporation to give the notice required under Section 4 of this Article II.