This study continues a series of the works on the development of the model (proposed by us) which describes the changes in the thermal and phase states of a high-temperature core melt in the cooled under-reactor crucible-type trap when the melt interacting with sacrificial material in severe reactor accidents at nuclear power plants. On the basis of the generalized formulation of the Stefan problem with free interfaces, an extended three-stage 3D model of the proceeding processes has been proposed, that takes into account the influence of various factors. The model includes a stage of inversion of oxide and metal components changing in the corium basin during thermochemical reactions. Approbation of the model was carried out by comparison between the obtained results and the data of the full-scale COPRA experiment on the heat transfer by natural convection in a corium basin with an internal heat source. Our calculation results using the COMSOL Multiphysics software package confirmed the efficiency of the proposed scheme for arrangement of the sacrificial material in the trap, as well the scheme for the trap’s cooling to provide the required target functions.