A method of molding and curing tires for vehicle wheels includes the steps of disposing a tire being processed on a toroidal support, enclosing the tire and the toroidal support inside a molding cavity defined in a vulcanization mould, pressing the outer surface of the tire against the molding cavity walls, and administering heat to the tire to cause molecular crosslinking of the tire. The pressing step includes the steps of compressing side portions of the tire between the molding cavity walls and the outer surface of the toroidal support, concurrently with the closing step, and imposing an expansion to a radially-outer portion of the tire to bring the radially-outer portion of the tire against the walls of the molding cavity.