Severe accidents in nuclear power plants are analysed in order to quantify the consequences of a core meltdown and fission products release. Such a multidisciplinary problem calls for a multiphase calculating process involving various tools. The first phase focused on the processes within the reactor core and the SCDAP/RELAP5 and MAAP4 codes were used for the analysis. Integral calculation was applied because the whole primary and secondary circuit of the power plant had to be modified in order to ensure the adequate thermal and hydraulic boundary conditions (pressure, temperature and the coolant flow). The results of the calculation defined the composition and mass of the molten material released in the lower plenum. The second phase was a combination of the CFD and FEM analyses of the lower plenum. The CFD analysis of the molten material natural circulation was conducted in order to define its configuration and temperature distribution. A detailed FEM model of the lower plenum was developed with the purpose of calculating the accurate temperature of the reactor vessel wall, which would help determine the precise time and place of vessel breach or meltdown. The radiation heat exchange between the molten material and the lower plenum structures has not been sufficiently studied. The core support plate is directly exposed to radiation heating. If overheated, it might collapse and cause the core and upper plenum structures to fall into the lower head. A radiation heat exchange model was implemented in the existing SCDAP/RELAP5 FEM COUPLE module and a core support plate model was developed. The results indicate the possibility of a plate rupture. A collapse of the remaining undamaged structures into the lower plenum would add extra burden to the reactor vessel and might eventually lead to its breach.