Abstract. The analysis of stress-strained state at the boundary «faced surface layer -substrate» is performed by methods of elasticity theory of inhomogeneous media, on exposure to the load distributed in a circle. The fundamental aspects of Kelvin -Helmholtz and Richtmayer -Meshkov instabilities are considered. The following methods are used for the research. The analytical method of solution is used for finding the temperature distribution of substrate and coating material as well as distribution of speed of material motion in deposition of the coating. Finite element method is required in accounting for the parameters of convective mixing. For the analysis of the proposed thickness and dispersion of the coating the concepts of hydrodynamic Kelvin -Helmholtz and Richtmayer -Meshkov instabilities are used. Using the mass, energy and momentum conservation laws, with allowance for the possible exothermal reactions, the system of equations of the mathematical model of electroexplosion synthesis on the basis of thermoreacting components of Ni-Al system is formulated. The degree of effect of model's parameters on dispersion and thickness of the coating is determined. The comparison of the modeling and experimental data is carried out. It is established that the due regard to the thermal effect of chemical reaction increases considerably the time of existence of the reacting elements in the liquid state and it facilitates the participation of the entire nickel in the reaction. The increased time of heat effect enables the other processes to occur more completely.