This work describes the computer model development of the water–water energetic reactor (VVER) 1000 nuclear power plant (NPP) in the methods for estimation of leakages and consequences of releases (MELCOR) 1.8.6 code and its subsequent use for the accident scenarios analysis leading to the core melting. The baseline accident scenario was a stress test case—the station blackout (SBO, the complete loss of alternating current electric power in a nuclear power plant). In addition to this, four other scenarios were analyzed in which the SBO was combined with other technological failures—the loss of steam generator feedwater system and small, medium, and large break coolant accidents (LOCA). The results provided detailed information on the time course of accident scenarios, their temperature and pressure parameters, hydrogen production, and the mass inventory released from the molten corium and debris into the containment of the NPP.