The author performed numerical simulations of several different surface coatings with the use of FEM. Several types of materials for the coatings were investigated like thermal barriers made of Al2O3 or ZrO2 and anti wear coatings TiN, TiC or TiCN. There were simulated coatings on the parts of a combustion engine like a piston as well as a valve. The were also performed investigations for the needs of fabrication of surgical tools coated with the use of DLC - diamond like carbon. The surface coatings were established on different substrates like steel, titanium, aluminum alloys or beryllium copper. The aim of the works is to establish the methods which can be useful in analyses of influence of heat treatment (i.e. heat impulse shocks) on the stress distribution in the area of coating-substrate system and on adhesion of the coating to the substrate. On the base of these works the review of surface coatings modeling will be presented: problems concerning the analysis of residual stresses distribution in the area of coating-substrate collaboration, the influence of the substrate shape, modeling in the macro and micro scale connected with the need of use of the different types of models, analyzing the coating-substrate system as a graded or functionally gradient material - FGM, building models with or without simulation of the microstructure imperfections like voids, roughness of the substrate and the coating as well as the bonds between particular surface layers.
The preliminary results obtained from micromechanical models of the ceramic FGM surface coatings with the linear function of the coating material volume fraction variation, show out the necessity of consideration in numerical simulations the residual stress relaxation mechanisms like development and joining of microcracks as well as the effect of presence and nucleation of the voids (on the way of plastic deformations). In the distance of barely several model grid domains there were observed the strong gradients of stresses which reach the extreme values from the calculated stress range.