Rubber compounds exhibit complex material behavior. Rate-independent and rate-dependent inelastic properties are observed. These features can be modeled by viscoelasticity and elastoplasticity as pointed out in the literature. As the tire in service is a rolling structure, it is of great importance to cover this situation in simulation approaches. Therefore, new and efficient formulations for steady-state rolling combined with viscoelastic and elastoplastic material models are presented in this paper. The specific constitutive characterizations are developed on the basis of generalized material formulations presented earlier in the literature by the author1. The underlying idea of the present procedures is to employ the material history, which is a function of time, as a function of space distributed over a ring of material points. In order to avoid very time consuming computations, approximations of the non-local material approaches are utilized. This way coupling terms along the ring of material points are suppressed and very efficient algorithms obtained. The models are presented in the context of steady-state rolling structures like a simple rubber ring and complex tire models.