An elevator includes a car, a counterweight, and a hoisting member connecting the car with the counterweight over a traction sheave. A free fall protection system includes a free fall protection controller, a free fall protection member connecting the car with the counterweight over the traction sheave or over a separate free fall sheave. The car and the counterweight are supported by the hoisting member in normal operation and by the free fall protection member only in a situation in which the hoisting member support fails. At least one free fall protection brake is arranged to stop the movement of the free fall protection member and thereby also the movement of the car and/or the counterweight, when being activated by the free fall protection controller.