A plant for building tyres, includes: a shaping work station configured for receiving a carcass sleeve; at least one radially expandable/contractible toroidal forming drum engageable in the shaping work station; at least one work station configured for building at least one component of a crown structure on a radially external surface of a tyre being processed, defined starting from the carcass sleeve that is shaped and coupled to the forming drum; transfer devices configured for moving said forming drum along a closed-loop completion path and arranging it in proximity to the work station in order to obtain a green tyre, the closed-loop completion path being extended from an initial work station to a final work station coinciding with the shaping work station; and a pick-up device configured for picking up said green tyre decoupled from the respective forming drum.