Reservoir rocks can exhibit very strong permeability (K) anisotropy. The classical anisotropy measurement methods, which consist of taking several plugs with differently oriented axes from a single core, or of taking measurements on samples with a particular shape, do not generally allow the permeability anisotropy to be fully defined. We have developed a simple, overall method to measure and characterize this anisotropy. If, at a point in a porous, permeable, infinite medium, totally saturated with a relatively incompressible fluid, a second fluid is injected that is perfectly miscible with the first, and has the same density, the interlace between these two fluids (i.e., the invasion front) describes a surface such that, at a given moment, the distance from the injection point to the surface is proportional to root K in the direction under consideration. To provide an overall quantification of the permeability of a medium, it suffices to describe the geometrical characteristics of an invasion front during a miscible displacement due to a pinpoint injection, and to measure a single absolute value of permeability. The proposed method consists of injecting a salt solution (e.g., KI) that absorbs X rays into a rock that has been previously saturated with brine; the resulting invasion front can be followed easily using X ray tomography. The method＇s validation is based on experimental verification that there is no disturbance due to ionic diffusion, that the results are insensitive to injection parameters, and there are no edge effects. The method has been applied to four rocks that are often studied in the laboratory, and whose permeability anisotropy is known from classical measurements. An excellent quantitative concordance is observed between CT scan results and conventional results, as long as the intrinsic heterogeneity of natural porous media as it affects permeability is taken into account. After smoothing raw data using a polynomial approximation, the experimental data are inverted in terms of the permeability tensor, using a method analogous to the one developed at Institut Francais du Petrole (IFP) for inverting the elasticity tenser. We will show an example based on a real reservoir case before concluding with a discussion of the applicability of this method to other scales of observation.