A machine (1) for the (stretch) blow moulding of bottles in polymeric material having a plurality of moulding units (10), each moulding unit (10) having a first half-shell (21) and a second half-shell (22), laterally hinged around a hinge pin (54) having a hinge axis (23), and a bottom (52) suitable for cooperating to cyclically form a closed cavity (24) suitable to receive a pre-heated pre-form and to allow the expansion by (stretch) blow moulding of the pre-form inside the cavity (24) so as to obtain a bottle, said moulding unit (10) being arranged to cyclically assume a closed mould configuration and an open mould configuration by means of opening/closing means (12) of the half-shells (21, 22) towards and away from a closure plane (X-X) passing through said hinge axis (23), and movement means (50) of the bottom (52), wherein said half-shells (21, 22) and said bottom (52) are actuated in a synchronized manner starting from a single motion inlet (36) comprising a single cam coupling.