A skydiving team called the Gypsy Moths visits a small town in Kansas to put on a show for the Fourth of July weekend. Their leader, Mike Rettig (Burt Lancaster), is accompanied by his partners, Joe Browdy (Gene Hackman) and Malcolm Webson (Scott Wilson).
The skydivers stay at the home of Malcolm’s uncle and aunt, John and Elizabeth Brandon (William Windom and Deborah Kerr). Distractions begin almost immediately when Mike becomes romantically involved with Elizabeth, whose husband overhears her making love with Mike in their home. Malcolm falls for local student Annie Burke (Bonnie Bedelia), a boarder in the Brandon house, while Joe takes an interest in a topless dancer.
Mike eventually asks Elizabeth to leave town with him, but she declines. During the next skydiving exhibition, Mike intends to do a spectacular “cape jump” stunt, but fails to pull the ripcord, which he intentionally fell to his death as he hits the ground upon impact at over 100 miles per hour. Although nobody wants to discuss it, there is a suspicion that he committed suicide. That night, Annie consoles Malcolm, and they make love. Before the team leaves for good, they have to bury Mike. To pay for the funeral, Malcolm does the same stunt that killed Mike. He leaves by train that night without attending Mike’s funeral.