The men were nabbed about 11:30 p.m. Monday when officers spotted them taking merchandise from the store, which has been closed since its roof collapsed in January.
Police did not identify the men because one gave officers a fake ID and other hasn't been charged with a crime, said police spokesman Sgt. Dean Politopoulos,
The suspect who provided the fake ID was charged with false personation, Politopoulos said.
Police are consulting with the District Attorney's office regarding charges for both men.
The accident occurred after the driver of a Bobcat-type crane that was doing repairs on the roof caused a sizable cave-in, leaving a hole estimated at approximately 40 feet.
Five people, including the operator of the Bobcat, suffered non-life-threatening injuries.
Click here to follow Daily Voice Mount Vernon and receive free news updates.