The hysteretic behavior of tire rubber compounds was investigated by tension/compression tests at different strains and strain rates, dynamic tests with varying frequencies and amplitudes, and tests with small cycle loading and unloading. According to these effects, a material model was developed that considers the complex frequency dependent (viscoelastic) as well as the rate independent (elastoplastic) inelastic behavior of filled rubber. This model combines different rheological elements representing viscous and plastic effects. The approach is valid for large strains. The hysteretic model has been implemented in an in-house FE code to analyze tire behavior assuming a constant driving velocity. The numerical algorithm is robust and shows excellent convergence, making it suitable even for large tire models. In computations for rolling tires, the consideration of the hysteresis yields a direct calculation of rolling resistance and energy dissipation, thus the new material law should prove useful in simulations of wear and durability.