The presence of discontinuities such as cracks and faults in porous media can remarkably affect the fluid pressure distribution. This is due to considerable contrast between hydraulic properties of porous matrix and discontinuity. Several numerical techniques have been adopted to simulate the behaviour of fractured porous media subjected to fluid flow mostly in the context of discrete fracture- matrix models. Current approaches still have several shortcomings, namely in terms of computational costs from large number of additional degrees of freedom to capture the discontinuities, and the implementation of special integration procedures. The present work proposes a new technique to model fluid flow in saturated fractured porous media based on coupling finite elements to enable embedding the preferential paths of flow created by discontinuities in regular meshes. The discretisation of fracture and porous medium does not need to conform and the meshes are coupled without additional degrees of freedom. Two numerical examples are presented to assess the performance of the new method in comparison with other techniques available in the literature.