A class of smooth approximations of the total friction force occurring on a plane finite contact surface is presented. It is assumed that the classical Coulomb friction law is valid on any infinitesimal element of the contact region. The models describe the stick phase, the fully developed sliding and the transition between these two modes. They take into account different values of static and dynamic friction coefficients. The models are applied in simulation of a dynamical system performing translational and rotational stick-slip oscillations, and then they are verified by comparison with the corresponding results in which an event-driven discontinuous model of friction is used.