The paper presents an application of a phenomenological material model for the viscoelastic stress response at large strains. The model is used for the simulation of carbon-black filled rubber in monotonic and cyclic deformation processes under isothermal conditions. The material stress response is decomposed into two constitutive parts which act in parallel : an elastic equilibrium stress response and a rate-dependent viscoelastic overstress response. The response of a particular filled rubber in the cyclic and relaxation tests was measured experimentally. The parameters of the constitutive functions are determined from the experimental data by an identification process employing nonlinear optimization methods. The paper concludes with a simulation by FEM of the cyclic loading of a simple rubber specimen.