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Regulation of the thermal and stress state of the “coating-base” system is an important step of the coatings quality management and is carried out by changing the thermal power of the plasma jet per unit of the sprayed surface by controlling the movement velocity of the plasma torch and the sprayed material flow rate. (Research purpose) The research purpose is development of a mathematical model that describes the process of layer-by-layer coatings formation and the change in the thermal state of the coating-base system during plasma spraying. (Materials and methods) We have used finite differences, finite elements and marching for solving the thermal and strength problems in internal stresses determining. We have used a technique for determining thermal fields, considering the dependence of thermal-physical and mechanical properties of the coating and base materials on temperature, the occurrence of plastic deformations and stress relaxation. A mathematical model has been designed for calculating a thermal field with a moving boundary considering the nonlinear nature of coating growth during layer-by-layer deposition and the dependence on the thermophysical properties of the coating-base system materials. We have substantiated the method that allows eliminating the existing shortcomings of traditional technologies for design and experimental studies of the thermal and stress state of the coating-base system, as well as automatization of the process of solving the numerical model and increasing the efficiency of the entire research cycle. (Results and discussion) It was found that when the flow rate of the sprayed material is changed from 0.1 to 1.0 grams per second and the plasma torch travel velocity is from 10 to 350 millimeters per second, the residual stresses in PG-19M-01 coatings on steel change their sign and can be both compressive and tensile. Varying the coating conditions allows reducing the level of residual stresses by 3-5 times. The article shows that a decrease in the level of residual stresses corresponds to an increase in the coating adhesion strength at a constant mass average temperature of the particles during the deposition process and is achieved by controlling the sprayed material flow rate and the plasma torch velocity, pre-heating the substrate and cooling. (Conclusion) It was found that the use of the proposed model makes it possible to evaluate the effect of the parameters of the spraying process (plasma torch travel velocity, spray material consumption, thermal state of the substrate before spraying, cooling conditions during spraying) on the residual stresses level.