The deformation of the free surface of the liquid pool in the VAR process may play a key role in explaining the apparition of surface defects on the ingot skin. In the present study, the deformation of the surface induced by electromagnetic stirring is investigated, for a simplified geometry, using CFD-based simulations, combining models for the turbulent fluid flow, heat transfer, free surface movements and electromagnetic forces. Particular attention is given to the implementation of thermal and electrical boundary conditions at the moving free surface. Verification of the developed model is carried out by comparison with the dedicated code SOLAR. The free surface dynamics of a liquid zirconium pool is then quantitatively analysed for different stirring procedures, and the effects of the stirring parameters (magnetic induction, reversal time) are predicted and discussed. The obtained results provide some insights into mechanisms by which surface deformation may influence the ingot skin solidification, leading to poor ingot surface quality.