An elevator rope comprising an elastomer coated, multistrand steel wire cable is claimed. In such a cable strands have a lay-length of at least 6.5 times the diameter of the bare cable diameter D. The cable is further coated with an elastomeric jacket, which adheres to the strands with a pull-out force not less than 15×D+15 newton per mm. The advantages of such an elevator rope are amongst others its limited elongation, its reduced diameter and its improved fatigue life.