A plant for building tyres for vehicle wheels, includes a sleeve building area in which devices for obtaining carcass sleeves operate, a crown building area in which devices for obtaining crown structures operate and a shaping station for shaping each carcass sleeve according to a toroidal configuration. Transfer devices for transferring the carcass sleeves from the sleeve building area to the shaping station, by means of a first translator configured for picking up each carcass sleeve from an outlet station of the sleeve building area, a second translator configured for releasing each carcass sleeve in the shaping station, and a storage device operatively interposed between said first translator and second translator.