In this paper we study two different model reduction strategies for solving problems involving single phase flow in a porous medium containing faults or fractures whose location and properties are known. These faults are represented as interfaces of dimension N − 1 immersed in an N dimensional domain. Both approaches can handle various configurations of position and permeability of the faults, and one can handle discretization grids that do not match up at the fault interface. For the numerical discretization we use the hybrid finite volume scheme as it is known to be well suited to simulating subsurface flow. Some results, which may be of use in the implementation of the proposed methods in industrial codes, are demonstrated.