Abstract: A 3D finite element model was developed to analyze magnetic field, electromagnetic force, current density, and the Joule heating field for electrodes, slag, and ingots in an electroslag remelting process with two series-connected electrodes. The proximity effect dominated in the two-electrode ESR system, while the skin effect was important in the single electrode system. Maximum current distribution occurred on the interior of two series-connected electrodes in the slag and 20 to 25% of total current went through the ingot. Maximum Joule heating was at the bottom interior of the slag electrode. Investigating the various parameters indicated that if current frequency exceeded 35 Hz, current density in the inner electrode tended towards a linear distribution. Maximum Joule heating in the slag increased with increasing electrode immersion depth and decreasing of slag cap thickness.