A theoretical solution is developed for the electromagnetic response of a two-dimensional inhomogeneity in a conductive half-space, in the field of a line source of current. The solution is in the form of an integral equation, which is reduced to a matrix equation, and solved numerically for the electric field in the body. The electric and magnetic fields at the surface of the half-space are found by integrating the half-space Green's functions over the scattering currents. One advantage of this particular numerical technique is that it is necessary to solve for scattering currents only in the conductor and not throughout the half-space.The response of a thin, vertical conductor is studied in some detail. Because the only interpretational aids available previously were scale model results for conductors in free space, the results presented here should be useful in interpreting data and in designing new EM systems. As expected, anomalies decay rapidly as depth of burial is increased, due to attenuation in the conductive half-space. Depth of exploration appears to be greatest for measurements of horizontal magnetic field phase, while vertical field phase is diagnostic of conductivity. Horizontal location and depth of burial are best determined through measurements of vertical or horizontal magnetic field amplitude.