A safety stop is provided for stopping a movable member having at least one set of opposed wheels for gripping a rail. The stop has a track on each of opposite sides forming a wedge shape of a narrow end progressively widening to a wide end in a direction of travel of the movable member. With the opposed wheels of the movable member respectively at opposite sides of the wedge shape member, the tracks of the wedge shape member engage and impart a spreading strain to the opposed wheels as the movable member moves in the direction of travel. The opposed wheels of the movable member comprise a deformable material to absorb the kinetic energy of the movable member. The tracks of the stop additionally may have undulating features comprising concave and convex surfaces in the direction of motion.