The mechanical and hydraulic properties of rock fractures are strongly influenced by surface conditions of the fractures. In this study, roughness heights of both surfaces of an artificially fractured rock were measured with a laser displacement meter, and then combined numerically to derive the apertures between the both surfaces. The spectrum of the surface roughness on a log-log plot is linear in a range of frequencies. In low frequencies, the power spectral density of the aperture variation is less than that of the surface roughness. The histogram of the apertures approximates a normal distribution because the measured fracture was considerably matched. The auto-correlation distance, being a length within which two points are spatially correlated with each other, of the surface roughness ranges between 1 to 4.5 mm, and that of the aperture variation is about 1 mm. To examine the effect of the auto-correlation distance of aperture variations on hydraulic properties of fractures, different auto-correlation distances were chosen, 20 aperture distributions for each auto-correlation distance were generated by using a personal computer and flow simulations were carried out. The simulations show that flow rates through fractures depend on not only the mean separation between the both surfaces but also the auto-correlation distance. In fractures composed of apertures with larger auto-correlation distance, the flow rates greatly vary fracture by fracture even in the same mean separations, and the average flow rate tends to approach the one predicted by the parallel plate model. When an aperture distribution has no auto-correlation, the flow rate could be uniquely estimated by the ratio of the mean separation between both surfaces to the standard deviation of apertures.