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Elleray attended Hutton Grammar School before earning a Bachelor of Science degree in Applied Mathematics from Durham University in 1979. After spending several years in the aerospace field, Elleray took a job with Tyrrell Racing in 1982 analyzing ground effect tunnels. In 1983 and 1984, he was involved with amateur racing teams before being employed as a designer and race engineer by Arrows F1. In 1999, he became Chief Designer for Bentley's prototype program.