Due to the revival of interest to the development of fast reactors cooled by liquid metals, the problem of carrying out theoretical research in support of their safety is actual. A detailed calculation of all stages of the accident from the beginning to the end requires knowledge of the laws for modeling physical processes occurring in the reactor in an emergency. The most serious are accidents with the destruction of the core. Simulation of severe accident in nuclear reactor is the key element in safety analysis of nuclear power plants. Destruction of fuel rods is one of the most important processes that should be calculated during core degradation. For different type of fuels the mechanism of the degradation are different too. For example, oxide and metallic fuels usually melt congruently at high temperature, but nitride fuel dissociates. The main objective of the proposed research is developing of models and numerical algorithms for calculation fuel rods destruction with oxide, metallic and nitride fuels. The models of the destruction processes and some calculation results are presented in the paper. The processes are investigated for the first phase of severe accidents covering the period from the onset of fuel-rod melting to the melt escape from the core center.