A hexahedral multi-block grid formulation for the modeling of two phase reservoir flows is developed and applied. Multi-block approaches are well suited to the modeling of geometrically complex features while avoiding many of the complications of fully unstructured techniques. Important implementation issues, including the accurate treatment of grid non-orthogonality and full tensor permeability (through use of a 27-point finite difference stencil), the treatment of exceptional cases arising when five blocks intersect, and a new well model which allows for the accurate resolution of near-well effects, are discussed. Solution efficiency issues, including the use of tensor splitting and the linear solution technique, are also discussed. The actual grid generation step is accomplished using a commercial package. Results for a variety of cases, involving flow through geologically complex systems and reservoirs with horizontal and deviated wells, are presented. Comparison with analytical results demonstrates the high level of accuracy of the 27-point formulation and the new well model. The method is also applied to a realistic example involving flow through a heterogeneous faulted system. This example illustrates the types of geometrically complex systems that can be modeled using the hexahedral multi-block approach.