A mathematical model to predict the cumulative failure distribution for the containment barrier system (CBS) employed in a deep geologic disposal facility is presented as a function of near-field environmental conditions expected at the Yucca Mountain site in Nevada. The model can address the effects of container design, areal power density, and dominant heat transfer mode on the cumulative container failure distribution. This model has been employed to describe the performance of the CBS as one part of a risk-based performance assessment of the Yucca Mountain site. The model employs Weibull and exponential distributions to describe container failures. Parameter values employed in the model are based on simple, time-dependent, mechanistic models and relevant corrosion data, which describe failure of individual components of the CBS as a function of environmental conditions. The relative importance of container design with respect to predicted container performance is demonstrated through comparison of the results for three candidate container designs. The best container performance was noted for the conduction-dominant heat transfer mode at an areal power density of 114 kW/acre for all container designs. Calculations for the titanium-clad, Alloy C-4 container design suggest that significant improvements in container performance may be achieved through the use of very high-performance alloys. The performance of the multipurpose container (MPC) design at the high areal power density (114 k W/acre) was only slightly better than the Alloy 825, single-barrier design. This was due to the potential deleterious effect of high-temperature oxidation on the carbon steel outer barrier of the MPC design.