The rupture of a thin liquid film is considered in the framework of an earlier developed mathematical theory of flows with forming/disappearing interfaces. The process is shown to be driven by the surface-tension gradient arising when the rate of variation of the free-surface area due to external disturbances becomes comparable with the inverse surface-tension relaxation time. The proposed mathematical description of the rupture phenomenon does not require the inclusion of intermolecular forces into the equations of macroscopic fluid mechanics.