A cylindrical bushing subjected to a stationary cyclic load is analysed with emphasis on the amplitude and frequency dependent damping and modulus. The material parameters were determined from a dynamic shear test, in terms of a viscoelastic-elastoplastic model. Using an overlay of finite element meshes, the material model was implemented in a finite element model of the cylindrical bushing and subjected to a radial cyclic load. The calculated damping and stiffness for the bushing were verified with measured data from the actual bushing. Results show that the viscoelastic-elastoplastic model used can be made to represent the amplitude and frequency dependence seen in the two natural rubbers investigated in this paper. It is also seen that the model, although fitted to a shear test, performs fairly well for a more general load case as well.