File a police report immediately with local law enforcement if your ID was stolen. Ask for a copy of the report and the name and contact information of the officer taking the report. You can show this type of documentation at the security checkpoint at the airport.
Arrive at the security checkpoint early and explain the situation to the officer at the document-checking station. If your ID was stolen, you should also bring a copy of the police report, if you filed one. The officer will then ask you to fill out a form that includes your full name and address. Officials will check this against all publicly available databases.
Prepare for additional screenings and interviews from local police and TSA (Transportation Security Administration) behavior-detection officers. You may also be required to submit to a whole-body pat-down, a body scan and a full luggage check before you are allowed to board you flight.
Check with the TSA agent at the entrance to security and see if they will accept other forms of photo ID you may have, such as a Costco Card, which has the member's photo embedded in the card, or a work photo ID.