The Electro-Slag-Remelting (ESR) is an advanced technology for the production of components of e.g. high quality steels. In the present study a comprehensive computational model using the VOF technique for the prediction of the slag/pool interface is presented for axisymmetric and steady state conditions. In this model the distribution of the electric current is not constant in time, but is dynamically computed according to the evolution of the slag and steel phase distribution. The turbulent flow, created by the Lorentz and buoyancy forces, is computed by solving the time-averaged mass and momentum conservation equations. The turbulence effect is modelled by using a k-model. Two numerical simulations were performed, one assuming a flat interface, and a second leaving the interface free to find an equilibrium shape. The results are then analysed and compared for both cases.