A crosslinked olefin elastomer foam has a specific gravity of 0.05 to 0.2, an expansion ratio of 8 to 15, a compression set of 30 to 60% and a tear strength of 1.5 to 2.5 kg/cm. The crosslinked foam is obtained by heating an elastomer composition comprising a specific ethylene/&agr;-olefin copolymer, an organic peroxide, a crosslinking auxiliary and a foaming agent. The crosslinked foam has a high expansion ratio, is free from surface roughening attributed to defoaming, realizes a soft touch, exhibits a low compression set and is excellent in mechanical strength (particularly tear strength) and heat resistance.