The paper presents a mathematical model and the results of calculating the process of melting of silicate materials as a result of their exposure to low-temperature plasma. In the case of a low temperature of the gaseous region exceeding insignifi cantly the silicate melting temperature, the phase transition is preceded by a quite long induction period characterized by the materials heating from the initial temperature to the melting temperature. After the completion of this stage, a melting process begins accompanied by a shift of the interphase boundary deeper into the material. With increase in the initial gas temperature the duration of the induction period decreases. It has been established that the velocity of the melting front propagation is determined by the initial temperature of the gas phase and the thermophysical characteristics of the material but is weakly dependent on the fi ll layer thickness.