As part of a complete theoretical description of the behaviour of the electric arc in the vacuum arc remelting process, a model has been developed for the column of plasma generated by a single cluster of cathode spots. The model combines a kinetic approach, taking into account the formation of the plasma in the cathodic region, and a hydrodynamic approach, describing the expansion of the plasma in the vacuum between the electrodes. The kinetic model is based on a system of Boltzmann-Vlasov-Poisson equations and uses a particle-type simulation procedure, combining the PIC (Particle In Cell) and FPM (Finite Point Set Method) methods. In the two-dimensional hydrodynamic model, the plasma is represented as a mixture of two continuous fluids (the electrons and the ions), each described by a system of coupled transport equations. Finally, a simplified method has been defined for calculating the electric current density and the energy flux density transmitted by the plasma to the anode. In order to achieve complete modelling of the electric arc in the VAR furnace, the movement of all the clusters on the cathode surface has been simulated, based on a detailed experimental study performed on industrial plant. The results of the numerical simulation presented are consistent with a certain number of experimental results available in the literature. In particular, the model predicts a percentage of the electric power of the arc transmitted to the anode (25%) in good agreement with the value indicated in the literature. (C) 2004 Kluwer Academic Publishers.