Captain Yossarian (Alan Arkin), a fictional U.S. Army Air Forces B-25 bombardier is stationed on the Mediterranean island of Pianosa during World War II. Along with other members of his squadron, Yossarian is committed to flying dangerous missions and after watching his friends die, he seeks a means of escape. Futilely appealing to his commanding officer, Colonel Cathcart (Martin Balsam), he finds that even a mental breakdown is no release when "Doc" Daneeka (Jack Gilford) invokes the "Catch-22" that the US Army employs. As explained, an airman "would be crazy to fly more missions and sane if he didn't, but if he was sane he'd have to fly them. If he flew them he was crazy and didn't have to; but if he didn't, he was sane and had to."

Trapped by the convoluted logic of the Catch-22, Yossarian watches as individuals in the squadron resort to other means to cope; Lt. Milo Minderbinder (Jon Voight) concocts elaborate black market schemes while crazed Captain "Aarfy Aardvark" (Charles Grodin) even commits murder. Following an attempt on his life, Yossarian flees the hospital and sets out in a raft, paddling to Sweden, a refuge for one of his other squadron mates who successfully escaped the madness.