A plant, a method and a process for building tyres for vehicle wheels in a carcass structure building line includes: a) associating a pair of support rings with a forming drum in a work station for associating support rings; b) building at least one structural component of the tyre being processed on the forming drum provided with the pair of support rings in at least one work station of the carcass structure building line; c) removing the pair of support rings from the forming drum in a work station for removing support rings; d) transferring the pair of support rings dissociated from the forming drum to a temporary storage for support rings; and e) building at least one further structural component of the tyre being processed on the forming drum without the pair of support rings in a work station of the carcass structure building line.