Abstract. In order to establish the safety of a disposl system for high-level radioactive waste, the system must be shown to satisfy radiological safety criteria imposed by regulatory agencies. In Canada, for example, the regulatory policy includes a quantitative limit on radiological risk to an individual for a period of 10,000 years following disposal. Mathematical modeling of the performance of the disposal system is essential to demonstrate that the system meets such quantitative criteria. There is considerable uncertainty in modeling the system because of the limited knowledge of both the geological environment of the disposal facility and the behavior of the engineered and natural components of the system far into the future. Procedures to reduce the uncertainty must be carried out during the entire life of the disposal project, and the uncertainty must be quantified to the extent possible. It is important that the limitations of the models be recognized, as well as their effectiveness in providing essential information in the siting, design, and regulatory process. A case study based on the concept proposed for the disposal of nuclear fuel waste in Canada demonstrates the use of mathematical modeling of a disposal system.