The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.