Abstract: The aim of cloth draping is to compute the rest state of a piece of cloth, possibly in contact with other solid objects, as quickly as possible. The context of free motion and very large deformations specific to cloth simulation makes the usual energy minimization schemes traditionally used in mechanical engineering inefficient. Therefore, most cloth draping applications only rely on dynamic simulation with ad hoc viscous damping or the dissipative behavior of numerical integration methods for obtaining convergence to the rest position of the cloth. We propose a "stop-and-go" technique which cuts out the velocity of the object at particular times for converging to the rest state, while taking advantage of the natural cloth motion toward equilibrium. This scheme can very easily complement any existing dynamical cloth simulation system, using either implicit or explicit numerical integration methods.