Rapson was born in 1914 in Alma, Michigan with a deformed right arm that was amputated at birth; he learned to draw expertly with his left hand. He learned architecture degrees at the University of Michigan, and at the Cranbrook Academy of Art, where he studied under Eliel Saarinen. “Cranbrook was a very exciting, dynamic place where I met and worked with guys like Charlie Eames, Harry Bertoia, and Harry Weese,” Rapson said.
As a young architect, Rapson worked for the Saarinen architectural office from 1940 to 1941. He moved to Chicago in 1941, where he worked with George Fred Keck and others.
- 1945: Case Study House No. 4, or "Greenbelt House" (part of the Case Study House program)
Esther McCoy famously wrote: "Rapson’s rendering of the house showed a helicopter hovering over the flat roof, as if the owner was coming home to the suburbs from his day at the office. His wife is waving to him. Where is she? Hanging out diapers in the drying yard. Rapson’s money was on the wrong machine."[7]
The "Greenbelt House" was constructed in 1989 for an exhibit at the Museum of Contemporary Art in Los Angeles.[8]
In recent years Rapson's firm developed a line of prefabricated modern houses called the Rapson Greenbelt, which grew out of a submission for the Dwell Home Design Invitational and are now available through a company called Wieler.