This paper has discussed the effective resistivity ellipse and the paradoxical phenomenon of anisotropy. Two cases have been discussed, namely: there are three measuring lines at arbitrary angles with one another and there are two mutually perpendicular measuring lines and an additional measurement of the transversal effective resistivity. For these cases, the paper has given the methods for quantitatively calculating the parameters of georesistivity anisotropy. The formulae given include those for calculating the azimuth (of the principal axis of minimum resistivityρ 1, the average resistivity (ρ 1 ρ 3)1/2, (ρ 2 ρ 3)1/2, and the anisotropy coefficientλ = (ρ 2/ρ 1)1/2. As a case history, the data observed by the Datong geoelectricity station have been processed with reference to the results ofin situ resistivity measurement in media subjected to shear. The results of analysis have led to the following understandings. Before and after the DatongM S6. 1 earthquake on October 19, 1989, the abnormal rise of NE-trending georesistivity and abnormal fall of NW-trending georesistivity observed at the Datong and Yangyuan stations were caused by the pure shear acting on the medium. The major principal compression was in NE-direction, which made an acute angle with the strike of the seismic fault plane, and thus there was a greater shear stress but very small normal stress so that the fault was likely to slide but the earthquake was only of moderate magnitude. The states of stress in medium were the same before and after earthquake and therefore the georesistivity precursor was of the same sign as that of co-seismic variations.