This study presents the results of modelling the rolling contact of the elastic sphere and the elastic half-space in the presence of a thin intermediate viscoelastic layer which properties are described by an elastic nonlinear Winkler body in the normal direction and a viscoelastic Maxwell body in the tangential direction. The analytical–numerical approach for the estimation of contact fatigue damage, accumulated in the elastic half-space under rolling friction conditions, is developed. The proposed model can be used, in particular, to study the effect of mechanical properties of the friction modifiers (elastic moduli and relaxation times) and its thickness as well as the relative slippage on the formation of the surface and under surface contact fatigue cracks in rails. The results of the analysis can also be applied for the estimation of efficiency of solid lubricants in rolling contacts under given operating conditions.