Abstract: To form a tire carcass, a body ply is wound about a drum, which has two half-drums movable axially in opposite directions to and from a center plane of the drum, and having respective turn-up bladders, on each of which is laid a respective annular lateral portion of the body ply; each annular lateral portion being turned up about a respective bead bundle and onto a sidewall of a toroidal-shaped annular central portion of the body ply by inflating the relative turn-up bladder and controlling distension of a given annular portion of the turn-up bladder so that, when inflation is completed, the annular portion assumes a given final position, in which an intermediate portion of the turn-up bladder rolls outwards along the relative sidewall of the annular central portion of the body ply.