Strands of steel bead wire or the like are individually surrounded with rubber and the rubber is then partially cured sufficiently by irradiation so that the rubber remains moldably plastic and the final cure will completely cure the rubber. Each bead core when completed is often enclosed in fabric. The completed bead assembly is incorporated in the carcass of a tire. When the tires, including the carcass, tread, etc., are cured, the rubber in the beads is completely cured and the beads are securely bonded to the balance of the tire.