A brake apparatus engages and locks a piston of a hydraulic elevator drive carrying an elevator car or a cable pulley. Attached at the upper end of a hydraulic cylinder guiding the piston is a beam on which are pivotally mounted at least two brake arms at pivot points. The brake arms are pivoted by a slidable plunger toward and away from the piston. Each brake are carries a brake lining having a shoulder formed on an inwardly facing surface providing a transition from a piston contact portion to a recessed portion of the surface. The shoulder is positioned in the same generally horizontal plane as the brake arm pivot point for initially engaging the surface of the piston to reduce forces transmitted through the brake arms during engagement and disengagement.