The variation of tensile strength and elongation at break of styrene-butadiene-styrene triblock copolymer containing 34.1, 40.0 and 52.5% styrene have been studied with respect to their morphology and the extent of crosslinking produced by irradiation with Co-60 rays. We assume that the existence of microphase separation between polybutadiene (PB) and polystyrene domains and entanglements between PB segments result in the unusual variation of the two characteristics with radiation dose, which is different from that in common elastomers and blends.