Abstract: A new algorithm for computing contact forces between solid objects with friction is presented. The algorithm allows a mix of contact points with static and dynamic friction. In contrast to previous approaches, the problem of computing contact forces is not transformed into an optimization problem. Because of this, the need for sophisticated optimization software packages is eliminated. For both systems with and without friction, the algorithm has proven to be considerably faster, simpler, and more reliable than previous approaches to the problem. In particular, implementation of the algorithm by nonspecialists in numerical programming is quite feasible.