Residual vibration in high-rise elevators remains an important issue. Our earlier work on this problem assumed fixed cable lengths. In this paper, we present a dynamic model of the elevator where the cable lengths are changing with time. The elevator car is modeled as a rigid body connected by two flexible cables. An elegant approach is presented here to modify the residual vibrations using the theory of /spl delta/-flatness. Collocation method is used to calculate the inputs required by the motors mounted at the ends of the two cables to modify the residual vibration. The approach is demonstrated by numerical simulation. An experiment is planned in. the near future to validate the theoretical results.