Abstract Sliding resistance of a rigid cylinder over a thin rubber layer due to rubber hysteresis is investigated. This problem underlies a model being developed for quantitatively accurate predictions of the performance of a new class of damping devices. As a full multiaxial constitutive law reflecting the amplitude-dependent behavior of filled rubbers is not available, this paper sets forth an approximate method of analysis which indirectly accounts for the material nonlinearity. Results of extensive finite element calculations are then reduced to compact material-independent forms which can be used as a universal design tool. Measurements of rolling resistance are also compared with theoretical predictions.