Elevator, which comprises at least an elevator car (C) and means for moving the elevator car, preferably along guide rails (G), and an overspeed governor arrangement, which comprises an overspeed governor rope (R,R',R''), which moves according to the movement of the elevator car, and which overspeed governor rope (R,R',R'') is connected to a brake arrangement that is in connection with the elevator car (C) such that with the overspeed governor rope (R,R',R'') force can be transmitted to the brake arrangement for shifting the brake (SG) comprised in the brake arrangement into a braking position. The rope comprises a power transmission part (2) or a plurality of power transmission parts (2), for transmitting force in the longitudinal direction of the rope, which power transmission part (2) is essentially fully of non-metallic material.