An elastic laminate having improved elastomeric properties is prepared by forming an elastic layer from a thermoplastic styrene block copolymer elastomer, crosslinking the elastic layer, and bonding the elastic layer to at least one nonwoven web. The elastic layer may be crosslinked before or after it is bonded to the nonwoven web. The elastic laminate combines the advantages of relatively low cost starting materials with the performance advantages typically associated with more expensive elastomers.