The present paper describes an overview of mathematical modelling of the glass melting process inside an open-top skull furnace having DC plasma discharge as the primary energy source. This melting system has been developed by Plasmelt Glass Technologies LLC (Boulder, CO, USA). A mathematical model of intensive glass melting, which is a non stationary state process, and corresponding software have been developed by a modelling team of Laboratory Glass Properties LLC (LGP). This mathematic model has been created in parallel with the development of the melting process itself. Having a fully operational pilot unit available from the Plasmelt team had the possibility to compare behaviour of a real melting system with that with that calculated by the model .