Purpose. The aim is to build a mathematical model of the electric arc of arc furnace (EAF). The model should clearly show the relationship between the main parameters of the arc. These parameters determine the properties of the arc and the possibility of optimization of melting mode. Methodology. We have built a fairly simple model of the arc, which satisfies the above requirements. The model is designed for the analysis of electromagnetic processes arc of varying length. We have compared the results obtained when testing the model with the results obtained on actual furnaces. Results. During melting in real chipboard under the influence of changes in temperature changes its properties arc plasma. The proposed model takes into account these changes. Adjusting the length of the arc is the main way to regulate the mode of smelting chipboard. The arc length is controlled by the movement of the drive electrode. The model reflects the dynamic changes in the parameters of the arc when changing her length. We got the dynamic current-voltage characteristics (CVC) of the arc for the different stages of melting. We got the arc voltage waveform and identified criteria by which possible identified stage of smelting. Originality. In contrast to the previously known models, this model clearly shows the relationship between the main parameters of the arc EAF: arc voltage Ud, amperage arc id and length arc d. Comparison of the simulation results and experimental data obtained from real particleboard showed the adequacy of the constructed model. It was found that character of change of magnitude Md, helps determine the stage of melting. Practical value. It turned out that the model can be used to simulate smelting in EAF any capacity. Thus, when designing the system of control mechanism for moving the electrode, the model takes into account changes in the parameters of the arc and it can significantly reduce electrode material consumption and energy consumption during smelting.