<p>This work is devoted to induction melting of heat-resistant nickel alloys, in particular, to the problem of stability of the oxidation film on the melt surface. The mathematical model describes heat and mass transfer in the metal melt in an alternating magnetic field and elastically stressed states of the film on the melt surface. The main equations of the problem and dimensionless parameters are presented. The states of the surface film are studied using numerical simulation. It is shown how a change in the magnetic field strength affects the flow of the metal melt at different frequencies. It is found that at different frequencies a change in the field strength leads to damping oscillations in the velocity field. The causes of these oscillations are discussed in detail. Loading and destruction of thin films during melt motion are considered. The mechanisms responsible for the primary destruction of the original film and of its fragments are revealed. Rupture of a quasi-stable film at different frequencies is investigated. It is shown that the result of the effect on the state of the film with an increase in the magnetic field strength depends on the field frequency. A frequency range has been found in which the surface film is strong enough to prevent intensification of the melt flow with increasing magnetic field strength. This effect ensures film stability.</p>