An unwed mother-to-be marries a total stranger so he can avoid the draft. She now has a father for her child and he doesn't have to go to Vietnam. But this marriage-of-convenience leads to a romance between the two.

Elwood P. Dowd's constant companion is Harvey, a six-foot tall invisible rabbit. To his sister, his obsession with Harvey has been a thorn in her plans to marry off her daughter. However, when she decides to put Elwood in a mental institution, a mix-up occurs, and she finds herself committed instead. It's now up to Elwood and "Harvey" to straighten out the mess.

Having both lost their jobs, two strangers become unlikely friends after a run in with a would be robber, who is actually a hitman with a grudge against the two.