Clay and granitic geologic rock units are potential host media for future repositories for used nuclear fuel and high level waste. This report addresses the representation of flow in these two media within numerical process models. Discrete fracture network (DFNs) models are an approach to representing flow in fractured granite that explicitly represents the geometry and flow properties of individual fractures. New DFN generation and computational grid generation methods have been developed and tested. Mesh generation and the generation of flow streamlines within the DFN are also included. Traditional form of Darcy’s law is not adequate for describing water flow processes in clay media. Non-Darcy flow behavior is incorporated in modeling, and a new relationship between water flux and hydraulic gradient was created by generalizing the currently existing relationships; an added empirical relationship between permeability and the threshold hydraulic gradient is presented.