The traction sheave elevator comprises an elevator car (1) moving along elevator guide rails (10), a counterweight (2) moving along counterweight guide rails (11), a set of hoisting ropes (3) on which the elevator car and the counterweight are suspended, and a drive machine unit (6) comprising a traction sheave (7) driven by the drive machine and engaging the hoisting ropes (3). The drive machine unit (6) of the elevator is placed in the top part of the elevator shaft (15) in the space between the shaft space needed by the elevator car on its path and/or its overhead extension and a wall of the elevator shaft (15).