The cars had to be brought in by crane because the front door of the RCA, next to the Royal Albert Hall in central London, is too small to allow them access. The only doorway big enough is off-road.
Among the cars was the Aston Martin Project Vantage, which was insured for pounds 1m before its 40-metre drop into the college. A two-seater sports car prototype, with a body and chassis constructed entirely from aluminium and carbon fibre, it is the work of a Scottish designer, Ian Cullum, an RCA graduate.
The exhibition, Moving Objects: 30 Years of Car Design at the Royal College of Art, opens next Thursday, 29 July.
Its co-director is the design guru Stephen Bayley. Mr Bayley said yesterday that he hoped the exhibition would make people rethink their attitudes to cars as works of art.
"We still think of a work of art as having a single author. But, like advertising, the car has acquired a lot of the functions of art," he said.
"In 1969, when the vehicle design course started, design was the poor relation of studio art and car design was a poor relation of a poor relation. In 30 years, the balance has shifted.
"Car design is certainly the most important thing the Royal College does economically, and maybe culturally as well. And this is an exhibition about design; it is not a motor show. It looks at the aesthetic, cultural and social aspects of car design. After architecture, cars are the things we see most of. The successful car design must be both pragmatic and poetic."
The exhibition will examine issues such as why some shapes sell and others do not, what our reaction is to colour and detail, and gender issues in car design.
The Royal College of Art runs one of only four vehicle design courses in the world. Two are in the United States. The other is at the University of Coventry.
Christopher Frayling, the rector of the RCA, said that since the Sixties, 200 cars had been designed by RCA alumni. He said all six members of the design team for the Hyundai car were former RCA students.