Rubber compounds exhibit complex material properties like rate-independent and rate-dependent inelastic characteristics. These features can be modelled by visco-elasticity and elastoplasticity as pointed out in the literature. A main application field of rubber is tire production. As a tire in service is a rolling structure, it is of great importance to cover this situation as well in simulation approaches in order to predict the structure's service characteristics during the development phase. Therefore, new and efficient simulation formulations for steady-state rolling combined with viscoelastic and elastoplastic material models are presented in this paper. The formulations are developed on the basis of generalized material descriptions presented earlier in the literature.