A rope brake for an elevator installation for braking a rope coupled to a car is provided, which has a stop that is immovable in the longitudinal direction of the rope and at least one brake shoe. The rope is led between the stop and the brake shoe, and the brake shoe is adapted to be moved back and forth between a braking position, pressing the rope against the stop, and a release position, releasing the rope. A drive coupled to the brake shoe is provided for releasing the rope. The drive is formed as a linear drive and the at least one brake shoe can be transferred by means of the linear drive into its release position against the action of a braking force acting on it in the braking position.