The quality of metallic materials depends on their composition and structure and these are determined by various physico-chemical and technological factors. To effectively prepare materials with required composition, structure and properties, it is necessary to carry out research in two parallel directions: 1. Comprehensive analysis of thermodynamics, kinetics and mechanisms of the processes taking place at the solid-liquid-gaseous phase interface during welding processes. 2. Development of mathematical models of specific welding technologies. We have developed a unique method of mathematical modeling of phase interaction at high temperatures. This method allows us to build models taking into account: thermodynamic characteristics of the processes, influence of the initial composition and temperature on the equilibrium state of the reactions, kinetics of heterogeneous processes, influence of the temperature, composition, hydrodynamic and thermal factors on the velocity of the chemical and diffusion processes. The model can be implemented in optimization of various technological processes in welding, surfacing, casting as well as in manufacturing of steels and non-ferrous alloys, materials refining, alloying with special additives, removing of non-metallic inclusions.