A method of cooling the molten core of a reactor, which consists in determining, after destruction of the reactor vessel by molten core, the location of the molten core debris and determining the state of core penetration by the information received from temperature sensors, cooling liquid volume supply to molten metal and adjustment, wherein after destruction of the reactor vessel by the molten core, the degree of destruction of the reactor vessel and the start time of the molten metal flowing out of the reactor vessel into the trap is determined, then coolant is supplied into the trap casing with a predetermined time delay, from the inspection chambers of the internal shells and the protective tubes unit of the reactor, after which the conditions for the formation of a sludge cap above the surface of the molten metal mirror are determined, the start time for the formation of a crust on the surface of the molten metal is determined, the completion time of aerosols release is determined, the completion time of vapour sorption and the time of hydrogen formation are determined, the stabilization time of the molten metal cooling processes and the time these processes exit into quasi-stationary mode are determined, then the volume of coolant supply is adjusted taking into account the thermal and physical parameters of the media in the sealed volume of containment, and then the volume of coolant supply is adjusted taking into account the minimum and maximum water levels in the reactor cavity.