Abstract: In this paper, The hydraulic conductivity of fracture is studied considering the geometry and topography of the fracture walls and asperity. Under low velocity and some restrictions on the magnitude of the roughness, an ideal model of fracture with wedge shapes and sinusoidal variation roughness is presented. The results show that the effective hydraulic aperture is less than the mean aperture and it depends on the standard deviation of the mean value of the aperture. At last, the effect on the flow pattern caused by the contact area is studied, the deviations of various experiential unit discharge formulas are analyzed, and the simple correction factors which depends only on the contact area. have been presented in this study.