A drum (1) for building tires (2), the drum (1) having two half-drums (12), each of which has an expandable bead clamping device (20), and at least one shaping bladder (27) and a turn-up bladder (33) fixed to an outer tubular body (16) of the half-drum (12) on opposite sides of the respective bead clamping device (20); each turn-up bladder (33) having an outer annular lip (34) extending, at rest, along the respective half-drum (12) and covering the respective bead clamping device (20) and substantially the whole respective shaping bladder (27).