An elevator has a car movable within a hoistway, a rack extending along the hoistway, the rack having a toothed profile with wave troughs and wave crests and a drive mounted in proximity to the rack so that the drive interacts with the rack to move the car. The drive includes a roller pinion unit fixedly mounted on a shaft and having a predetermined number of roller pinions arranged in a circle around the shaft and extending parallel to the shaft. The roller pinion unit interacts with the toothed profile of the rack. The drive also includes a motor unit configured to rotate the shaft. Optionally, the drive includes a brake unit configured to act on the shaft.