The processes that occur at the solid electrode-electrolyte interface and in the discharge gap during surface treatment with a vapor-gas discharge are a set of various interrelated phenomena, such as physical, chemical and electrochemical ones. The main physicochemical phenomena that determine the process of processing metal surfaces are the electric field, modes of heat and mass transfer between the processed metal surface and the liquid medium (electrolyte). Due to the large number of physical parameters that significantly affect the processing of a part, difficulties arise in planning and conducting experiments in order to optimize the technology for processing metal surfaces. This problem can be solved using mathematical modeling, which allows you to explore various processes and phenomena at no additional cost. The proposed mathematical model will be useful both at the stage of processing the measurement results and in preparing for the experiment.