 Peter (Vittorio Gassman), a WW II  displaced person  about to be deported jumps ship in New York harbor in an effort to find an ex-G.I named Tom (Jerry Paris)whom he helped during the war and can prove Peter s right to legal entry in the United States. It is a race against time for if he can t Tom within 24 hours and prove his case, he will be branded a fugitive and will be permanently disqualified for U.S. citizenship. His quest leads him to befriending Maggie (Gloria Grahame), a down-on-her-luck factory worker whom he rejuvenates through his good faith; a visit to a jazz club where Shorty Rogers and his band and trombonist Jack Teagarden are playing, and an interlude with a good- hearted burlesque dancer, Tanya Zakoyla (Robin Raymond), takes him to her mother s home (Else Neft) for food and rest. The climax comes at dawn in the United Nations building (the "glass wall" of the title) where he goes to plead his case and that of all displaced persons.