The invention relates to an elevator provided with a coated hoisting rope (9), in which elevator a hoisting machine engages a set of hoisting ropes by means of a traction sheave (5), said set of hoisting ropes comprising coated hoisting ropes (9) of substantially circular cross-section which have a load-bearing part twisted from strong steel wires (16). The cross-sectional area of the steel wires (16) of each hoisting rope is larger than about 0.015 mm2 and smaller than about 0.2 mm2, and the strength of the steel wires (16) is greater than about 2000 N/mm2. Moreover, the core of each hoisting rope (9) consisting of steel wires (16) is coated with a substantially thin sheath (17) softer than the core, forming the surface of the hoisting rope.