The present study aims to understand the melting of the consumable electrode in the VAR process and gain some insight into the influence of an ensemble arc motion on the melting behaviour. In a previous study, a 2D axisymmetric model of the heat transfer in the cathode had been developed. Using the operating parameters as model inputs, it enabled prediction of the melt rate and the evolution of the melting area. Model results were successfully compared to melt rate measurements in an industrial VAR furnace. In recent years, it has been claimed that the electric arc may not be considered as steady and axisymmetric. Our experimental investigation of the luminosity recorded during an actual VAR heat confirms that a transient 3D behaviour may take place. Therefore, a 3D version of the previous model was set up to predict the heat transfer and melting of the electrode, using the unknown ensemble arc motion as an input. The arc is assimilated to a transient distribution of energy flux density. Results evidence that the influence of the arc motion on the shape of the electrode tip can be very important. In industrial practice, the cathode tip usually remains relatively flat during melting. The shapes of the computed electrode tips enable us to propose some arc parameters which remain compatible with both the periodic behaviour of the light emitted and the flatness of the electrode.