The invention concerns a unit (6) for molding containers (2), comprising: a pair of half-molds (9), mounted respectively on two supports (10) mobile in horizontal translation; a primary transmission (19) controlling the movement of the supports (10); a mold base (14) mounted on a support (15) mobile in vertical translation; a secondary transmission controlling the movement of the mold base support (15); a locking device (16), comprising two mobile locks (17) co-operating each with a half-mold support (10); a tertiary transmission (21) controlling the movement of the locks (17). The transmissions include cams mounted on a common shaft, respectively coupled to the half-mold supports, to the mold base support and to the locks.