The invention concerns an elevator system comprising an elevator car (3) with a working platform (6) arranged for carrying people or materials and which by means of the interaction between a gear wheel and gear rack can be moved along an elongated generally vertical mast (1) constructed from a number of mast sections (2) mounted on top of each other. To facilitate the erection, tearing down and anchoringof the mast to a nearby building structure, the moving unit (1) comprises a passenger-carrying service and assembly platform (10), which, via a swing arm (16), is flexibly supported by the elevator car to allow a swivel action in a horizontal plane (C, D) relative to the elevator car (3).