Investigated in the paper are the mechanisms of deformation and fracture of a material with coatings of different thicknesses. Boundary-value problem in the plane-strain formulation is solved numerically by the finite-difference method. Microstructure of the composite is taken into account explicitly in calculations. The value of stress concentration near the “coating-base material” interface is found to increase nonlinearly with decreasing the thickness for thin coatings, and the value changes but only slightly for different thicknesses of thick coatings. This effect is observed at the elastic stage of composite deformation, intensifies as plastic deformation develops in the base material, and amounts to 25% at the prefracture stage. Recommendations which could be useful for optimization of the coating thickness are proposed.