A model is developed for sliding and rolling friction that can be used in simulations of dynamic systems involving mechanical elements that are subject to friction. Sound bases for the model are developed around the hypothesis that the origin of friction is in quasi static contact bonds that are continuously formed and subsequently broken. Sliding friction, including coulomb friction and the so-called 'stiction,' as well as rolling friction are believed to be realistically simulated by the model. The model has been proven to accurately simulate transient torque and rate measurements on ball bearings tested in the laboratory.