Hydraulic conductivity (or intrinsic permeability) determined in a standard permeameter is biased if the anisotropy is not taken into account. This bias can be a significant source of error in the characterization of any type of aquifer or reservoir. Theoretical arguments show that it is possible to determine the complete permeability tensor of a sample by measuring the average filtration velocity and the average gradient vectors during steady state flow experiments. The full permeability tensor is calculated with a linear least squares algorithm. To date, a prototype has been built that shows promising results, but the level of accuracy of the measurements is not yet sufficient to fully demonstrate its applicability. The primary advantages of this new technique are that no preliminary assumptions with respect to the principal directions of anisotropy are required prior to testing and that it does not require sophisticated test equipment. ¿ 2001 American Geophysical Union