Process for building tyres for vehicle wheels, comprising: arranging a carcass sleeve comprising at least one carcass ply and two beads on a shaping drum comprising two half-drums and two supports , wherein each of the beads is supported by one of the two half-drums , wherein each support is operatively associated with one of the half-drums and carries a plurality of application levers having free ends facing towards the respective half-drum ; toroidally shaping the carcass sleeve supported by the two half-drums ; applying sidewalls on opposite sides of the carcass sleeve ; wherein applying the sidewalls comprises: arranging each sidewall as a ring around the application levers of a respective support , making an axial appendage of said sidewall protrude axially beyond the free ends of the respective application levers ; radially opening the free ends of the application levers of each support so as to make the respective sidewall radially expand, wherein said axial appendage remains radially more contracted with respect to the remaining portion of the sidewall and converges towards a rotation axis (X) of the shaping drum ; axially approaching the free ends of the application levers of each support to the respective half-drum up to engaging said axial appendage with the carcass sleeve ; further and radially opening the free ends of the application levers of each support up to overturning the respective sidewall and making it adhere against a side of the carcass sleeve . arranging a carcass sleeve comprising at least one carcass ply and two beads on a shaping drum comprising two half-drums and two supports , wherein each of the beads is supported by one of the two half-drums , wherein each support is operatively associated with one of the half-drums and carries a plurality of application levers having free ends facing towards the respective half-drum ; toroidally shaping the carcass sleeve supported by the two half-drums ; applying sidewalls on opposite sides of the carcass sleeve ; wherein applying the sidewalls comprises: arranging each sidewall as a ring around the application levers of a respective support , making an axial appendage of said sidewall protrude axially beyond the free ends of the respective application levers ; radially opening the free ends of the application levers of each support so as to make the respective sidewall radially expand, wherein said axial appendage remains radially more contracted with respect to the remaining portion of the sidewall and converges towards a rotation axis (X) of the shaping drum ; axially approaching the free ends of the application levers of each support to the respective half-drum up to engaging said axial appendage with the carcass sleeve ; further and radially opening the free ends of the application levers of each support up to overturning the respective sidewall and making it adhere against a side of the carcass sleeve . arranging each sidewall as a ring around the application levers of a respective support , making an axial appendage of said sidewall protrude axially beyond the free ends of the respective application levers ; radially opening the free ends of the application levers of each support so as to make the respective sidewall radially expand, wherein said axial appendage remains radially more contracted with respect to the remaining portion of the sidewall and converges towards a rotation axis (X) of the shaping drum ; axially approaching the free ends of the application levers of each support to the respective half-drum up to engaging said axial appendage with the carcass sleeve ; further and radially opening the free ends of the application levers of each support up to overturning the respective sidewall and making it adhere against a side of the carcass sleeve . <EOS>