The mold press includes a drive arrangement for controlling press movement and closure force. The drive arrangement includes a pair of generally identical drive units connected between upper and lower press plates adjacent opposite longitudinal ends of the press. The drive units in a preferred embodiment each employ a ball-screw drive arrangement. The screw shaft extends vertically between the top and bottom press plates. The screw shaft engages a ball nut mounted on one press plate, typically the bottom press plate which is disposed for movement toward and away from the top press plate. A first high speed drive arrangement employing a first electric motor is coupled to the screw shafts for effecting high speed opening and closing of the bottom press plate. A second low-speed driving arrangement including a second electric motor is drivingly connected to the ball-nut assemblies for permitting low-speed but high-torque driving of the nut units for final closing of the press and application of the desired press force. Each drive unit has the screw shaft resiliently supported for limited axial displacement relative to the upper press plate so that, when the second drive system is activated to effect final closure of the mold, one or the other of the screw shafts can be axially displaced a small amount if necessary so as to permit full closure between the opposed upper and lower mold parts even though irregularities may cause one longitudinal end of the mold parts to contact and close prior to the other longitudinal end.