An apparatus and method for braking a carriage which travels on rails of an inclined or vertical elevator. The elevator includes a cable driving device having cables connected to the carriage for moving the carriage along the rails. The carriage has a main frame assembly and a movable frame assembly, mounted to slide along the main frame assembly. The braking device comprises a cam disk assembly having eccentric disks rotatably mounted to the movable frame assembly and held in a first position at a predetermined distance away from a surface of each of the rails for frictionally engaging the rails when released from the first position. The cam disk assembly then causes a plurality of brake blocks of the brake device to engage frictionally the rails when the eccentric disks frictionally engage the rails. A first releasing device causes the eccentric disks to release from the first position and engage frictionally the rails when at least one of the cables breaks. Moreover, a second releasing device causes the eccentric disks to release from the first position and engage frictionally the rails when the carriage travels above a predetermined speed. Finally, at least one shock absorber damps relative movement between the movable frame assembly and the main frame assembly, when the brake blocks engage the rails, to stop movement of the carriage along the rails.