It happened in the 14400 block of New Falls of Neuse Road at 1:20 p.m.
Police say 51-year-old Scott Randall Gray has been charged with with two counts of robbery with a dangerous weapon. One of the counts relates to the robbery of the bank and the second concerns the theft of a motor vehicle as he fled the scene.
Police said Gray entered the bank, announced the robbery, and said he had a bomb in a bag he was carrying.
They say after he took the money, Gray demanded the keys to a car in the parking lot. A bank customer surrendered the keys, and the Gray fled in the car.
A short distance from the bank, Gray apparently changed vehicles and entered a second vehicle. That vehicle was stopped a short time later by Wake Sheriff's Office deputies near the intersection of Six Forks and Strickland Roads.
Investigators treated the bag left behind as a possible bomb until it was determined to be safe.
Police kept people back and bank employees were evacuated as a precaution.
Gray is being held at the Wake County Detention Center.