Abstract: The TPU of this invention contains unsaturation in its polymeric backbone. The unsaturation can be present in the soft segment or in the hard segment or in both the soft and hard segments of the TPU. The TPU can be molded like a thermoplastic, and can be subsequently crosslinked by exposure to electron beam irradiation into thermoset articles having excellent chemical resistance, dimensional stability, set properties, heat resistance, oxidative resistance, and creep resistance. In one embodiment, the TPUs of this invention are the reaction product (1) a hydroxyl terminated intermediate, (2) a polyisocyanate, (3) a saturated glycol chain extender, and (4) a glycol chain extender containing carbon-carbon double bonds, such as the allyl moieties present in trimethylolpropane monoallyl ether.