Estimation of potential radionuclide releases from the waste package subsystem of a nuclear waste repository is required for two reasons: (a) to judge whether the engineered barrier system complies with the performance regulations prescribed by the U.S. Nuclear Regulatory Commission; and (b) to provide radionuclide source terms needed to predict the isolation performance of the natural barriers (i.e., geologic medium), which must be compared with the U.S. Environmental Protection Agency safety standard. A probabilistic approach developed at the Basalt Waste Isolation Project (BWIP) for the estimation of radionuclide releases from a proposed nuclear waste repository in basalt is presented. The central idea of this approach is that uncertainties in both the radionuclide transport parameters and the random nature of container failures impact the estimation of release rates. Details of the method are provided that account for both sources of uncertainty. Sample applications are presented that are based on preliminary data. Briefly, the BWIP methodology consists of (a) a container corrosion model, (b) a model describing the random sequence of container failures in time, (c) a stochastic transport model to obtain the probability distribution of releases from a single container failing at a specified time, and (d) a model to integrate the releases from the randomly failing containers in the repository.