Flow through the fracture is usually estimated by cubic law, which assumes flow to occur between two parallel plates. The cubic law is valid to represent the flow through the fracture system if the matrix permeability is very low to provide any significant flow contribution. However, in high permeability rocks, the flow occurs through both fracture and matrix systems. Flow through matrix may sometimes exceed that through the fractures under increased stress acting on the reservoirs. Under these circumstances, the cubic law should be modified by combining the weighted average of the permeabilities in order to account for flow through matrix. In this paper we present the amount of flow through fracture and matrix system based on modified cubic law equations by conducting a series of laboratory experiments on fractured cores under different stress conditions. The flow rate through fracture and matrix system and the pressure drop were matched using simulation. X-ray CT was used to determine the fracture aperture and saturation distributions. In addition, the saturation distributions from simulation results were compared to X-ray CT Scan results.