We present a unified treatment for modeling Coulomb and viscous friction within multi-rigid body simulation using the principle of maximum dissipation. This principle is used to build two different methods—an event-driven impulse-based method and a time stepping method—for modeling contact. The same principle is used to effect joint friction in articulated mechanisms. Experiments show that the contact models are able to be solved faster and more robustly than alternative models. Experiments on the joint friction model show that it is as accurate as a standard model while permitting much larger simulation step sizes to be employed.