This article discusses the mathematical description of the physical processes of transformation of composite substances of a plasma jet. A mathematical model describing the propagation of elastic waves in a three-component medium was developed for the prediction and planning of the use of plasma deposition technology, in particular in the study of the kinematic characteristics of the plasma flow. Also in the course of mathematical modeling the table of coefficients of compressibility of liquid (plasma jet) and gas and velocities of longitudinal and transverse elastic waves is obtained. Graphs of the velocity of propagation of longitudinal and transverse waves in the plasma coating material on its physical and mechanical characteristics-compressibility coefficients are plotted.

In a three-component medium, when it is de-formed, acceleration waves propagate longitudi-nally on the wave surface. In this paper, the be-havior of acceleration waves and their influence on the quality of the propagation medium during the formation of composite coatings during plasma spraying were investigated. A flowchart has been compiled to create a software product that promotes theoretical studies of wave pro-cesses in a three-component environment.