Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

General Dynamics Corporation:

We consent to the incorporation by reference in the registration statement on Form S-8 regarding the General Dynamics Corporation 401(k) Plan for Represented Employees of our reports, dated February 8, 2013, with respect to the consolidated balance sheets of General Dynamics Corporation and subsidiaries as of December 31, 2011 and 2012, and the related consolidated statements of earnings (loss), comprehensive income (loss), cash flows, and shareholders’ equity for each of the years in the three-year period ended December 31, 2012, and the related financial statement schedule and the effectiveness of internal control over financial reporting as of December 31, 2012 which reports appear in the December 31, 2012 annual report on Form 10-K of General Dynamics Corporation.

We consent to the incorporation by reference in the aforementioned registration statement on Form S-8 regarding the General Dynamics Corporation 401(k) Plan for Represented Employees of our report, which appears on Form 11-K, dated June 25, 2012, with respect to the statements of net assets available for participant benefits of the General Dynamics Savings and Stock Investment Plan for Represented Employees as of December 31, 2010 and 2011, and the related statements of changes in net assets available for participant benefits for the year ended December 31, 2011.

/s/ KPMG LLP

McLean, Virginia

February 8, 2013