An apparatus for manufacturing tires for vehicle wheels wherein each tire includes a carcass structure formed starting from at least one carcass ply laid on a forming support extended along a longitudinal axis. The apparatus includes at least one device for positioning at least one annular anchoring structure on at least one end edge of the carcass ply, the positioning device being circumferentially extended around the longitudinal axis of the forming support and axially movable with respect to the forming support between an operating position distal from the forming support and at least one operating position close to the forming support. The apparatus further includes a device for turning up the end edge of the carcass ply around the annular anchoring structure, the turning up device being circumferentially extended about the longitudinal axis of the forming support and axially movable for approaching/moving away to/from the forming support. The positioning device and the turning up device are radially expandable/contractible in a synchronous manner with respect to the longitudinal axis of the forming support and are settable in a plurality of different operating radial positions, each operating radial position being selected based on a respective radial dimension of the tire to be manufactured.