Abstract: A method for building a radial tire on a tire-building machine that has an expandable carcass drum with a cylindrical external circumference and two bellows supports with inflatable bellows. A tire inner liner and a carcass ply have projections and project beyond the edges of the carcass drum are laid and spliced on the carcass drum. The bead cores with core profiles are positioned and the projections of the carcass ply are turned up around the outsides of the bead cores by the inflation of the bellows. Expandable bellows supports are provided that are expanded for the placing and splicing of tire components so that the external surfaces of the bellows together with the external surface of the expanded carcass drum form at least essentially a uniform cylindrical load-bearing surface.