[en] If a core meltdown accident is postulated to occur, a large mass of molten fuel and steel debris could collect at the bottom of the reactor vessel. As a consequence, the vessel would be subjected to rapid heating and surface melting. In the absence of adequate cooling, inelastic failure or meltthrough could occur. The two dimensional thermal response of the vessel was obtained from a multireigion ADI solution of the fully implicit finite difference analogues of the governing differential equations. These equations have been transformed into a coordinate system moving with the melting surface. All non-linear effects such as the surface boundary conditions were included using an iterative scheme with quasi-linear equations. (Auth.)