In this paper we present a new model for flow in fractured porous media. We formulate our model in terms of a coupled system of boundary integral equations and present an efficient procedure for solving the equations using the boundary element method. In the new model, the flow in the matrix is governed by the usual Darcy law for porous media, with the fractures being treated as planar sources embedded in the matrix. The flow in an individual fracture is governed by a two-dimensional Darcy law (as in a Hele-Shaw cell), with an associated planar sink distribution. The essential feature of this approach is that the fractures are treated as special planes rather than narrow-gap voids. The error in the resulting system of equations is on the order of an intrinsic dimensionless parameter (the ratio of the fracture gap size to the scale of the volume under consideration). We also describe how we adapt the new model to compute effective grid block permeabilities. This was the principal motivation behind the development of the new model. Using effective grid block permeabilities to model flow in fractured oil and gas reservoirs is a much more efficient process than modeling the flow when every fracture is precisely represented. We present some numerical examples that illustrate the new flow model and how it is used to model flow in a reservoir.