Snell won the Wolf Prize in Medicine in 1978. He won the Nobel Prize in Physiology or Medicine in 1980 with Baruj Benacerraf and Jean Dausset. They won it "for their discoveries concerning genetically determined structures on the cell surface that regulate immunological reactions". Snell specifically "discovered the genetic factors that determine the possibilities of transplanting tissue from one individual to another. It was Snell who introduced the concept of H antigens."