Investigations of processes associated with the disruption of cooling of the reactor core and possible subsequent destruction and melting of the core have become of paramount importance in connection with the stricter safety requirements for operational and planned nuclear power plants. It is necessary to know how to correctly describe the scenario of the development of accident situations, to characterize quantitatively accident processes, to predict the probable consequences of accidents, and to develop methods and technical means for decreasing undesirable consequences.Boiling of liquid-metal coolant in the fuel assemblies of a fast reactor is one of the uncalculated operating regimes of a reactor and can arise as a result of a decrease of the coolant flow rate, increase of power production, and other reasons. Overheating of the coolant in the fuel assembly (and, as a consequence, boiling of the coolant) is also possible after accidental reactor shutdown, when the core is cooled. In the process, the power released corresponds to the residual energy release, and the coolant either stops moving or it moves as a result of natural convection.Boiling of the coolant as an accident situation, characterized by a large difference of the specific volume of the vapor and the liquid, is a strong perturbative factor, which gives rise to a sharp restructuring of the hydrodynamics of the entire flow. as a result of which the flow becomes unstable. The character of boiling of a liquid metal (sodium) in the core of a fast reactor and. primarily, the propagation velocity of the steam phase determine the rate of increase of the positive reactivity in the reactor core. Further development of the accident process depends on the amount of energy released as a result of the increase of reactivity because of the boiling of the hquid metal.In some countries (Japan, Germany. USA, France, and Great Britain) long-term programs of experimental and computational thermal-hydraulic investigations of the development and consequence of accident situations in a liquid-metalcooled reactor core have been conducted since the 1970s. Attention was focused mainly on the investigation of the dynamics of the development of the vapor phase m a fuel assembly, the character of the cooling during boiling of the coolant in the region behind the blockage in the fuel assembly, and so on. For example, staged investigations of accident processes accompanied by boiling of a liquid-metal coolant in ring-shaped channels and multirod assemblies with a duration of not more than 10 sec (power increase, decrease of the flow rate, blockage) were conducted in Japan [1][2][3][4][5]. In Germany nonstationary processes associated with the study of a loss of coolant accident and blocking of part of the flow section of the fuel assembly were investigated [6, 7]. In France investigations of boiling of the coolant in a fuel assembly under stationary conditions, during slow transient processes with a decrease of the flow rate, natural convection, fast processes with an increase...