Radionuclides released from a vitrified waste package after overpack failure spread into the buffer material surrounding the waste package, then migrate through different pathways into the water-bearing fracture in the rock surrounding the high-level radioactive waste repository, and transport through the faults to the biosphere. The buffer material has low permeability and the solute is transported through the engineered barrier system by diffusion only. In the water-bearing fracture, the problem is of the convection diffusion type with highly varying parameters from one medium to the other due to the variability in length, transmissivity, and other transport-relevant properties of the transport paths. This complex geometry is modeled using the wavelet Galerkin approach. The Wavelet Integrated Repository System (WIRS) wavelet-based system is an integrated tool to calculate the transport of single or radionuclide chains in both near and far fields of the repository system. The model, which is a very coarsely discretized wavelet based, is devised to be very fast since the scaling functions, which are used as a basis function, are compactly supported. Only finite numbers of the connection coefficients are nonzero, and the resultant matrix has a block diagonal structure that can be inverted easily. One of the main problems encountered in solving the model for the radionuclide transport in the geospheric media is the treatment of the boundary and interface conditions. In order to maintain the integrity of the system, the boundaries of the wavelet series are shifted until the end is independent of any expansion coefficients of the scaling function that affect the solution within the real boundaries. WIRS agreed well with models using a very detailed discretization. Accuracy is gained with the proper selection of wavelet-dilation orders pair. WIRS has been applied to the Japanese high-level radioactive waste repository concept where the migration is through different barriers and pathways. Single and decay chain radionuclide release calculations have shown the capability of WIRS to handle different situations rapidly and easily.