Results of mathematical modeling of the melting process of silicate materials in a plasma reactor are presented. Quartz sand containing up to ~98 wt% SiO 2 was used as a model material. It has been found that in the initial period of time at the temperature T f = 2500 K of the air-plasma medium, the gas temperature near the phase interface is below the melting temperature. As a result of heat exchange in the gas phase, the thermal energy is transferred first from the central and then from the upper layers of the material to the phase interface. If the thermal energy in the gas phase turns out to be sufficient for the phase transition, then melting begins after some time. When the initial temperature increased to T f = 3000 K, melting begins almost instantly (t m = 0.2 s). In this case, the constant temperature slightly exceeding the melting temperature is established at the phase interface. It has been showed that the velocity of the melting front propagation is determined by the initial gas phase temperature and the thermal and physical characteristics of the material, but weakly depends on the thickness of the filling material layer.