The invention relates to an elevator system comprising a first elevator car, a second elevator car, a rotatable rope wheel mounted on a fixed location, and a roping suspending the first and second elevator car on opposite sides of the rope wheel, the roping comprising at least one rope passing over the rope wheel, and connected on the first side of the rope wheel to the first elevator car and on the second side to the second elevator car. Said rope comprises at least one load bearing member oriented parallel with the longitudinal direction of the rope made of composite material comprising reinforcing fibers embedded in polymer matrix, which reinforcing fibers are carbon fibers oriented parallel with the longitudinal direction of the rope.