A new discrete-fracture multiphase flow model developed allows incorporation of fractures in a spatially explicit fashion. It is an alternative to conventional dual-porosity, dual-permeability models used most often to model fractured subsurface systems. The model was applied to a water flood on a 2-D random fracture network. A standard Galerkin finite element method was used to discretize the domain; triangular elements were used for matrix and line elements for the fractures. The finite element formulation was validated by using a commercial finite difference simulator. Results from a simple discrete-fracture model agreed reasonably well with the explicit fracture representation of the same domain. At low permeability contrasts between the matrix and the fractures, the model, as expected, predicted approximately symmetric water advance. At high permeability contrasts, the fracture network played a critical role in determining water advance and oil recovery. Significant oil bypassing was observed, particularly at higher flow rates. The oil recovery was determined by a complex interplay of the absolute matrix permeability, permeability contrast and flow rates. Fracture capillary pressure also played a significant role in determining water penetration in the matrix.