An inching drive system for a mechanical press including a hydraulic motor and gear mechanism, that engages the flywheel of the press. The hydraulic motor is mounted for rectilinear movement toward and away from the flywheel for selective engagement therewith and includes a gear that meshes with teeth on the periphery of the flywheel. A separate hydraulic piston/cylinder arrangement moves the inching drive system into and out of engagement with the flywheel.