Abstract: The present invention is about a traction sheave elevator, without the machine room, comprising an elevator car that runs on guide rails placed in the shaft and connected to at least one hoisting rope un-coiling on a diverting pulley driven by a traction sheave. The invention's characteristic consists in comprising a space, outside the elevator shaft, which houses, at least partially, the traction sheave and is equipped with an opening near a floor's door for the access to the drive machine and to the traction sheave, from outside the shaft. The invention also provides for arranging the two diverting pulleys on the counterweight and on the elevator car in a way that one or the other can be tilted with respect to the vertical or arranging them on the same axis and on the same body of the pulley with the grooves of the alternating hoisting ropes.