A new vitrification process based on a cold crucible heated by direct induction has been developed by CEA. This process is characterized by the cooling of all the walls and by currents directly induced inside the molten glass. This paper presents a global modelling of phenomena which take place in vitrification in a cold crucible. Electromagnetic, thermal and hydrodynamic phenomena are modelled within the molten glass. The thermohydrodynamic aspects are solved by FLUENT software (distributed by Fluent France) and the electromagnetic aspects by OPHELIE (EPM program based on integral methods). The numerical studies are validated using experimental results obtained from pilot vitrification facilities.