A process is provided for manufacturing radial tires for a motor vehicle having a radial carcass, a reinforcing structure with at least two layers of criss-crossed symmetrically arranged metallic cords forming a belt, and a tread. The process involves a series of steps which comprise: building up a carcass in a cylindrical configuration on a first expandable building drum and shaping the carcass into a toroidal configuration. A reinforcing belt is also formed by winding two layers of metallic cords on an auxiliary expandable drum with a diameter equal to the external diameter of the toroidal shaped carcass. The belt is maintained in slidable contact on the drum and shaped toroidally by expanding the auxiliary drum. The belt is then removed from the auxiliary drum and transferred with a tread band to the carcass on the first drum. The carcass is toroidal shaped again to assemble the carcass and belt. The assembly is vulcanized under pressure in a mold.