Purpose. The authors propose to develop a mathematical model for the calculated determination of residual stresses in arbitrary layer of a thermal gas coating based on the change magnitude in the base geometry (sample deflection) and the variation law of the layer thickness derivative, further regulation of these stresses by changing the technological parameters of spraying for each type of sprayed coating. Methodology. Based on known works on stress detection of in welded joints, the approach of determination of samples deflection after layer-by-layer spraying was developed. These deflection parameters are the basis for the developed mathematical model of influence on the stress state. The data on the study of the main types of residual (internal) stresses, as I type, distributed in the volume of the whole part (sample) with coating, and II type, localized in the volume of sprayed particles, are systematized. Findings. We presented investigations of the residual stresses arising in the applied layer, the magnitude and nature of the distribution of which depend on the type, base and sprayed materials, methods and parameters of spraying, the rigidity of the part, and other factors. The important role of evaluating residual stresses in a thermal gas coating by the calculation method is shown in connection with the complexity of the experimental determination of the kinetics of stress development in the coating-base composite. Originality. The authors of this work, on the basis of the first created mathematical model and software product Mathcad-Prime 6 2020, conducted a study of the level and principles of the formation of residual stresses in the coating during gas-thermal layer-by-layer spraying with various material, including the possibility of using a pulsating spraying air flow. Analytical studies have shown that the attention in the literature over the past five to seven years has been paid only to the study of residual stresses and deformations in welded joints, and only the growing interest in spraying technology opens up wide possibilities for studying the formation of stress fields in a thermal gas coating. Practical relevance. The results obtained in this paper confirm the formation of residual stresses in coatings and can be used as computational programs to solve design tasks, as well as for educational purposes during experts training in engineering fields.