Two auxiliary support members are operatively engaged with a building drum, in axially approached relationship with respective halves of the drum itself, each auxiliary member having a circumferential rest surface extending in the continuation of an outer circumferential surface of the building drum itself. Applied around the outer circumferential surface of the building drum is at least one carcass ply having axially opposite end flaps each lying on the circumferential rest surface of the respective auxiliary support member. A pair of auxiliary shaping members engaged with the building drum in place of the auxiliary support members, each act against a circumferential abutment edge carried by the building drum, to enable the carcass ply to be shaped into a toroidal configuration concurrently with mutual approaching of the halves of the building drum.