Method, process and plant for building tires for vehicle wheels wherein: in a service position of a carcass structure building line, a forming drum is associated with a pair of support elements including a first support element and a second support element; the forming drum is moved, associated with the pair of support elements, in a deposition line in the carcass structure building line; and the forming drum is transferred from the deposition line to a subsequent work station of the carcass structure building line. The transfer from the deposition line to the subsequent work station includes dissociating the forming drum from the second support element, keeping the forming drum associated with the first support element; transferring the forming drum, associated with the first support element and dissociated from the second support element, to the subsequent work station; dissociating, in the subsequent work station, the first support element from the forming drum, leaving the forming drum in the subsequent work station; and transferring the first support element, dissociated from the forming drum, into the service position.