The development of power plants focuses on increasing the parameters of water coolants up to a supercritical level. Depressurization of the unit circuits with such a coolant leads to emergency situations. Their scenarios can change significantly with the variation of initial pressure and temperature before the start of depressurization. When the pressure drops from the supercritical single-phase region of the initial thermodynamic parameters of the coolant, either the liquid boils up, or the vapor is condensed. Because of the rapid pressure decrease, the phase transition can be non-equilibrium that must be taken into account in the simulation. In the present study, an axisymmetric problem of the outflow of a water coolant from the pipe butt-end is considered. The equations of continuity, momentum and energy for a two-phase homogeneous mixture are solved numerically. The vapor and liquid properties are calculated using the TTSE software package (The Tabular Taylor Series Expansion Method). On the basis of the computer complex LCPFCT (The Flux-Corrected Transport Algorithm) the program code was developed for solving numerous problems on the depressurization of vessels or pipelines, containing superheated water or gas under high pressure. Different variants of outflow in the external model atmosphere and generation of waves are analyzed. The calculated data on the interaction of pressure waves with a barrier are calculated. To describe phase transitions, an asymptotic relaxation model of nonequilibrium evaporation and condensation has been created and tested.