The results of estimation of the nature and magnitude of residual thermal stresses in CuO oxide layer synthesized on a substrate of pure copper using a known analytical model for calculating thermal stresses in single-layer coatings are presented. Thermal stresses can lead to deformations and destruction of thin-film structures and coatings, shortages and reduced quality of parts on which they are applied. The main technological parameters, on which the values of thermal stresses depend, are the operating temperatures of the process of formation of thin-film oxide layers. After the synthesis process, the coated substrates are cooled to ambient temperature. This cooling leads to thermal residual stresses. In the case where the coefficient of thermal expansion of the material of the oxide layer is much less than the coefficient of thermal expansion of the substrate material, in the CuO layer compressive residual stresses generete, while in the Cu substrate – tensile stresses. The stress-strain state during the cooling of the thin film/substrate system, which is free from external forces, was investigated. The mathematical model used the assumption that the resulting deformations do not exceed the elastic limit (the residual stresses lie in the region of elastic deformations), and the temperature gradient in the thickness of the materials does not change. It should also be noted that the values of thermal expansion coefficients, modulus of elasticity and Poisson's ratios are constant values and do not depend on temperature changes. The paper presents the main analytical dependences of thermal stresses on the physical and mechanical properties of the coating materials and the substrate. Based on the results of calculations, a graph of the dependence of thermal stresses of the coating-substrate system depending on the temperature of synthesis of oxide layers was developed. Thermal stresses are one of the components of the total residual stresses operating in the film/coating system. The obtained results on the values of residual stresses can be used to prevent the deformation and failure of thin films and coatings, as well as to predict the characteristics of the surface layers.