A driver and a mechanic travel around the United States hopping from drag strip to drag strip in a 1955 Chevy Bel-Air coupe. They race for money, betting with their competitors. The pair gains a young and talkative female stowaway. Along the way they unintentionally attract a well-to-do drifter driving a new Pontiac GTO. This older man, looking for attention, antagonizes their efforts.

The U.S. submarine Anthony Wayne is underway for a top-secret mission. Onboard is a highly classified device that will give the Americans a decided nuclear advantage. The entire mission and the secret technology are threatened when the sub commander discovers his crew has been infiltrated by enemy agents. The commander is charged with trying to protect the device while ferreting out the enemy agents. Compounding matters is the state of the commander's physical and mental condition, which is being questioned by his crew.