SUMMARYThe oxidation of the zircaloy cladding of fuel rods in nuclear reactors, important during a severe accident, is governed by the di!usion of oxygen in solid zirconium. The latter exists in many phases which depend on the content of oxygen and have di!erent di!usion coe$cients. Discontinuous changes in oxygen concentrations occur at the phase boundaries, which also move in the course of di!usion, obeying an equation similar to the Stefan condition in heat transfer problems with phase change. We have devised and implemented a scheme for 1-D problems using the "nite-di!erence approach, which involves setting the di!usion coe$cient to zero in &forbidden' concentration ranges. The method is shown to be mathematically equivalent to the enthalpy formulation for the Stefan problem. With a boundary condition at the vapour/solid interface which takes into account steam di!usion and dissociation, the code is applied to analyse the phenomena of steam starvation and the dissolution of the oxide layer, which are relevant to severe accidents.