Most of the Earth's crust contains fluids, and fractures are common throughout the upper part. They exist at a wide range of scales from micro-fractures within grains to major faults and shear zones that traverse the crust. In this paper, the stress-dependent permeability in fractured rock masses have been investigated considering the effects of nonlinear normal deformation and shear dilation of fractures using a two-dimensional distinct element method program, UDE. A new analytical and numerical model was proposed to determine the relationship between fracture dip angle, aperture and permeability. The numerical work were conducted in two ways: (1) increasing the overall stresses with a ﬁxed ratio of horizontal to vertical stresses components; and (2) increasing the differential stresses (i.e., the difference between the horizontal and vertical stresses) while keeping the magnitude of vertical stress constant. The results showed that at the stress ratio of 1 the signiﬁcant shear dilation occurs at an approximately low stress and mean fracture angles. For the differential stresses case, the shearing process can result in breakage of the asperities, resulting in the decrease of the dilation rate and strain softening of the fracture.