The “safety case” approach has been developed to address the issue of evaluating the performance of a geologic repository in the face of the large uncertainty that results for evaluations that extend over hundreds of thousands of years. This paper reviews the concept of the safety case as it has been defined by the international community. We contrast the safety case approach with that presently used in the U.S. repository program. Especially, we focus on the role of uncertainty quantification. There are inconsistencies between the initial proposal to dealing with uncertainties in a safety case and current U.S. practice. The paper seeks to better define the safety case concept so that it can be usefully applied to the regulatory framework of the U.S. repository program.