Coatings are increasingly used to improve the mechanical and tribological behavior of surfaces. It is necessary to develop models to guide the initial choice of coating/substrate combinations that can withstand the applied loads. A three-dimensional model of an elastic multilayered body, loaded both normally and tangentially against an elliptical rigid body (partial sliding, rolling/sliding conditions), is presented here. This model is based on linear elasticity theory, integral transforms, Fast Fourier Transform, and unilateral contact analysis with friction. Normal and tangential contact conditions between the two bodies are first determined and then used to calculate the multilayered body stress field. One application is given here: The influence of the mechanical properties of coating and substrate, as well as coating thickness, is studied on contact conditions, internal stresses, and potential failure mechanisms.