In this paper, we obtained the analytic solution of the three-dimensional problem of elasticity concerning non-homogeneous half-space, in which the surface is under normal and tangential loading applied in a circular area. Half-space is composed of the homogeneous body, as well as coatings containing two homogeneous layers: interlayer and top layer. The analysis was carried out in cases where the Young's modulus of the intermediate layer differed from the Young's modulus of the substrate and the top layer. We have concentrated on first principal stress analysis. The obtained results can serve as an indication for the design of the composition of coatings in the context of tensile stress.
Keywords: double-layer coating; normal loading; shear loading; three-dimensional problem of elasticity.