Abstract: An improved method and apparatus for rapidly forming plastic foam shells from a flexible foam sheet. The foam sheet is intermittently passed through a radiant heating unit and is rapidly heated on both sides to 130.degree.-250.degree. F. to soften the foam. The heated foam sheet is immediately passed through a forming die unit in which the foam sheet is deformed partly into the die cavity by withdrawal of air from the cavity, and a die plug descends and final forms a shell while rapidly cooling the foam shell to below its plastic deformation temperature. By this forming method and apparatus, ethylene-containing foam shells having a depth 10-25 times the foam sheet initial thickness are rapidly formed at 10-30 cycles/minute.