Whereas the elastic Hertzian contact force with nonlinear damping gives rise to the overlap dynamics in the discrete element method, the precise physical meaning of tangential springs representing solid friction has remained obscure. Moreover, the well-known difference between the static and the sliding friction coefficient has often been ignored. In the present paper, the recently derived linear continuous spring–dashpot–slider model is generalized for viscoelastic spheres, where the spring stiffness and damping depend on the overlap and its time derivative. It compares favorably to the force–displacement relations obtained from the viscoelastic continuum theory. Both the linear and the generalized, non-linear model readily lend themselves to an efficient implementation of the difference between static and sliding friction coefficients. Their application in a simulation of chute flow quantifies the errors incurred, if one assumes that static and sliding friction coefficients were equal.