Films and coatings are used for an enormous and diverse set of applications including mechanical, electronic and optical devices, protection at high temperature, cutting tools enhancement and automotive use. Many of these applications require the various properties associated with inorganic and metallic / non-metallic materials; i.e., with ceramics. Therefore, a large number of coatings have been developed and used for a long time in the various fields, especially in mechanical one. As one of the mutual surface actions, the problems of contact stresses are complex. The relationship between load and stress are nonlinear. Besides, the material is often apt to deform plastically under low load. However, analytical solutions exist only for some simple problems. If a material has a complicated shape or inhomogeneous properties, numerical method must be used. In this paper, the analysis of the contact stress of the coating layer was solved, using the finite element method.