Hole-to-hole resistivity measurement is a useful method of detecting deeply buried fractures and ore deposits in the subsurface. With drilling costs continually rising, there is a growing need for developing methods of borehole geophysics such as this. In this study, we present theoretical results relating to detection of thin oblate spheroids and ellipsoids with arbitrary attitude.If we assume that individual fractures within a fracture zone are connected to each other and are of finite lateral and vertical extent, then we can model the fracture zone as a thin conductive oblate ellipsoid or spheroid with arbitrary orientation of the major axis. Detection of such deeply buried fracture zones is the object of this study. Here the effects of the surface of the Earth are neglected and the body is assumed to be enclosed within an infinite homogeneous mass. The surface of the body is divided into a series of subsurfaces, and a numerical solution of the Fredholm integral equation is applied. Once a solution for the surface charge distribution is determined, the potential can be specified anywhere by means of Coulomb's law. The theoretical model results indicate that cross-borehole resistivity measurements are a more effective technique than single-borehole measurements for delineating resistivity anomalies in the vicinity of a borehole. In some cases, the depth to the center of the body and the dip and strike of the major axes of the body can be estimated.