Machine for forming containers (3a), comprising a unit (2) for extruding plastic tubes (3), a blowing unit (5), a mould for containing the containers (3a), formed by two half-moulds (4a, 4b) movable, upon actuation of associated first means (100), in a longitudinal direction (X-X) and symmetrically with respect to a fixed axis (Z-Z) perpendicular to said longitudinal direction, the unit formed by the mould (4) and by the associated first actuating means (100) being movable, upon actuation of second actuating means (200), in a transverse direction (Y-Y) from a first position, in substantial alignment with the extrusion unit, into a second position, in substantial alignment with the blowing unit, and vice versa, said second means (200) for actuation of the mould (4) in the transverse direction comprising at least one linear motor (210, 220).