We study experimentally and numerically the permeability of a rough fracture at laboratory scale when viscous forces are dominating (low Reynolds number). The experimental setup includes a granite fracture surface (10¿10 cm2) opened in mode I. It allows a continuous opening of the fracture parallel to its mean plane. The fracture roughness is measured and characterized in terms of self-affine heterogeneities. Its isotropy is checked. The departure from the cubic law is measured as a function of the aperture opening (for mean separations between 4.0 and 10.3 mm) and the pressure drop orientation by rotating the fracture by 90 degrees. A strongly anisotropic hydraulic behavior is observed and results from the geometrical heterogeneities that exist up to the fracture macro-scale. ¿ 2000 American Geophysical Union