Undetectable Firearms Modernization Act of 2013

Undetectable Firearms Modernization Act of 2013 - Amends the Undetectable Firearms Act of 1988 to extend such Act for 10 years.

Revises what are prohibited firearms to include any firearm: (1) that, after removal of all parts other than major components (currently, of grips, stocks, and magazines), is not as detectable by walk-through metal detectors as the Security Exemplar; or (2) any major component of which, if subjected to inspection by the types of detection devices (currently, x-ray machines) commonly used at airports for security screening, would not generate an image that accurately depicts the shape of the component.

Modifies the definition of: (1) "major component" to include the barrel of a firearm only in the case of a rifle or shotgun; and (2) "Security Exemplar" to repeal the requirement that it be fabricated within 12 months after enactment of such Act.

Exempts from undetectable firearms provisions: (1) a prototype firearm for detectability testing; (2) any firearm received by, in the possession of, or under the control of the United States; or (3) the manufacture, importation, possession, transfer, receipt, shipment, or delivery of a firearm by a licensed manufacturer or licensed importer pursuant to an existing contract with the United States. (Replaces the exemption of any firearm that has been certified by the Secretary of Defense [DOD] or the Director of Central Intelligence [CIA] as necessary for military or intelligence applications or that is manufactured and sold exclusively to U.S. military or intelligence agencies.)