Accident sequences which lead to severe core damage and to possible radioactive fission products into the environment have a very low probability. However, the interest in this area increased significantly due to the occurrence of the small break loss-of-coolant accident at TMI-2 which led to partial core damage, and of the Chernobyl accident in the former USSR which led to extensive core disassembly and significant release of fission products over several countries. In particular, the latter accident raised the international concern over the potential consequences of severe accidents in nuclear reactor systems. One of the significant shortcomings in the analyses of severe accidents is the lack of well-established and reliable scaling criteria for various multiphase flow phenomena. However, the scaling criteria are essential to the severe accident, because the full scale tests are basically impossible to perform. They are required for (1) designing scaled down or simulation experiments, (2) evaluating data and extrapolating the data to prototypic conditions, and (3) developing correctly scaled physical models and correlations. In view of this, a new scaling method is developed for the analysis of severe accidents. Its approach is quite different from the conventional methods. In order to demonstrate its applicability, this new stepwise integral scaling method has been applied to the analysis of the cerium dispersion problem in the direct containment heating.