Accurate analyses of the hydrogeology of fractured rock require an understanding the flow characteristics of single fractures. It is well known that these flow characteristics are strongly controlled by fracture apertures. Recent investigations on the distribution of apertures in natural fractures suggest that the cubic law can accurately predict the fluid flux through rough-walled fractures as long as the appropriate average fracture aperture is used. Combining the stochastic cubic law with a simple deformation model results in a nonlinear relationship between fracture hydraulic and mechanical aperture. This relationship is shown to be consistent with published experimental and numerical data above a critical minimum aperture. Below this minimum aperture, the transmissivity of the fracture is approximately constant. Results have implications for the interpretation of laboratory fracture flow data and raise important questions pertaining to the mechanics of fracture deformation below the critical minimum aperture. ¿ American Geophysical Union 1995