The support cooperates with the half-molds (2, 3) of a molding unit used to shape a container from thermoplastic material. This support comprises: a pedestal in the form of an actuating cylinder (11), the rod (12) of which is solidly connected to the mold base (1); and, between the rod (12) of the actuating cylinder (11) and the mold base (1), an assembly system (13) formed by a female part in the form of a nut (14) and of a male part in the form of a screw (15). The nut (14) is trapped at the end of the rod (12) of the actuating cylinder (11) and the screw (15) is associated directly or indirectly with the mold base (1). A system of shim(s) (40, 41) can be used to adjust the working stroke of the rod (12) of the actuating cylinder (11) as required.