A defense-in-depth engineered barrier system (EBS) is employed in the current design concept for the potential high-level nuclear waste repository at Yucca Mountain, Nevada, USA. Simplifying the geometry of the cylindrical waste container into the equivalent spherical configuration, and incorporating detailed analysis of the mechanics of water flow around the waste container surface, a mathematical model is developed for advective release from a “failed” (or perforated) waste container under dripping water. It is shown that the advective release rates are controlled by diffusion through the perforations in the waste container, and affected insignificantly by the dripping flow rate for the flow rate range considered. The release rates depend strongly on the number of perforations (or pit penetrations) in the waste container. The insensitivity of the release rate to the dripping flow rate is explained by the fact that radionuclide is released from the container surface to the boundary layer of the water film which contacts the container surface and is relatively stagnant. Also, since a laminar flow around the waste container surface is assumed in the model development, radionuclides transport across the water layers in the film by diffusion only. Additionally, the insignificant effect of the flow rate is contributed by the “short” penetration depth of radionuclide into the water film assumed in the model development. The analyses show that the number of perforations, the size of perforation, the container wall thickness, and the geometry (i.e., radius) of the waste container are important parameters that control the advective release rate. It is emphasized that the “failed” (or perforated) waste package container can still perform as a potentially important barrier to radionuclide release.