An analytical solution and a finite element calculation have been utilised to investigate the contact stresses due to elastic spherical indentation into coating/substrate systems. Such calculated stress distributions may be used for the optimal design of layer systems as well as, together with experimental penetration-force curves, to determine quantitative measures for toughness and adhesion of the film. Both approaches were compared using various systems composed of a higher modulus surface coating on a relatively low modulus substrate. It was found that both methods agree very well and yield adequate stress distributions for various film thicknesses. Here we show the radial stress component Yy = sigma(r) for six different systems.