Fractures often control subsurface fluid flow and efforts to predict near-surface fluid flow typically focus on quantifying the relative influence of aperture and surface roughness on transmissivity. At greater depths, lithostatic and tectonic stresses play an increasingly important role in controlling fracture transmissivities. For the case of well-correlated fracture surfaces, such as those expected in new tensile fractures, fracture transmissivities quickly become negligible as a normal stress is applied to the fractures. However, if these fracture surfaces are displaced in shear, the fractures remain open and conductive at much higher stresses. Shear displacement of two well correlated or perfectly mated surfaces leads to anisotropy in the correlation structure of the fracture aperture field. In the presence of large normal stress, it is likely that only fractures subjected to some shear displacement will remain conductive, and thus, they are likely to exhibit some degree of anisotropy. Predicting the degree of anisotropy requires quantifying the combined influence of surface roughness, shear displacement of the fracture surfaces and the applied normal stresses. We use previously tested computational models to explore the influence of shear displacements of fracture surfaces subjected to a sequence of normal displacements (increasing stress) on transmissivity both parallel and perpendicular to the shear displacement of the surfaces. Results suggest that normal deformation of displaced fracture surfaces can lead to an order of magnitude increase in the anisotropy ratio from that observed in the unstressed fracture. These results suggest that the influence of normal stress on fracture anisotropy must be considered when implementing effective-continuum or discrete-fracture-network representations of fluid flow through fracture rock masses.