Process for building tyres for vehicle wheels, comprising the steps of: forming a carcass sleeve on a building drum , comprising at least one carcass ply having end flaps engaged with respective annular reinforcing structures incorporated in respective beads; picking up the carcass sleeve from the building drum ; engaging the carcass sleeve on a shaping drum ; toroidally shaping the carcass sleeve carried by the shaping drum to couple it with an outer sleeve comprising a belt structure, wherein picking up the carcass sleeve comprises: arranging the building drum carrying the carcass sleeve in a coaxial and axially centred position between two gripping members mutually side by side and coaxial with respect to an alignment axis (X-X) wherein each gripping member comprises: an annular support ; a plurality of coupling elements carried by the annular support and circumferentially distributed around the alignment axis (X-X); wherein each coupling element has a support stem slidably engaged with the annular support of the respective gripping member , and a gripping protrusion which protrudes axially from the support stem towards the other gripping member ; gripping each of the beads of the carcass sleeve by means of said plurality of coupling elements carried by each of the gripping members ; contracting the building drum to disengage it from the carcass sleeve retained by the coupling elements . forming a carcass sleeve on a building drum , comprising at least one carcass ply having end flaps engaged with respective annular reinforcing structures incorporated in respective beads; picking up the carcass sleeve from the building drum ; engaging the carcass sleeve on a shaping drum ; toroidally shaping the carcass sleeve carried by the shaping drum to couple it with an outer sleeve comprising a belt structure, wherein picking up the carcass sleeve comprises: arranging the building drum carrying the carcass sleeve in a coaxial and axially centred position between two gripping members mutually side by side and coaxial with respect to an alignment axis (X-X) wherein each gripping member comprises: an annular support ; a plurality of coupling elements carried by the annular support and circumferentially distributed around the alignment axis (X-X); wherein each coupling element has a support stem slidably engaged with the annular support of the respective gripping member , and a gripping protrusion which protrudes axially from the support stem towards the other gripping member ; gripping each of the beads of the carcass sleeve by means of said plurality of coupling elements carried by each of the gripping members ; contracting the building drum to disengage it from the carcass sleeve retained by the coupling elements . an annular support ; a plurality of coupling elements carried by the annular support and circumferentially distributed around the alignment axis (X-X); wherein each coupling element has a support stem slidably engaged with the annular support of the respective gripping member , and a gripping protrusion which protrudes axially from the support stem towards the other gripping member ; gripping each of the beads of the carcass sleeve by means of said plurality of coupling elements carried by each of the gripping members ; contracting the building drum to disengage it from the carcass sleeve retained by the coupling elements . <EOS>