Elstree Studios:The bulk of the film was shot at Elstree apart from three specific scenes which overflowed into Shepperton.
Shepperton Studios:Three scenes (The Massassi Temple ceremony at the end of the film, the Rebel Briefing Room and the monitoring of the attack on the Death Star scene) were shot at Shepperton, due to the larger H Stage being needed for the temple scene. The main base of the film was Elstree Studios.
The Lot / Warner Hollywood Studios:After returning from England, George Lucas reshot some sequences at Samuel Goldwyn Studios.
Cardington Airship Sheds:One of the sheds was used as the exterior of the Massassi Temple, heavily disguised by a matte painting. The interior of the shed can be seen beyond the matte painting.