The numerical method of Lines and Jones for investigating the problem of the perturbation of alternating geomagnetic fields by three-dimensional conductivity inhomogeneities embedded in a layered Earth is extended to include models in which vertical discontinuities may extend to the grid boundaries. The case considered is that in which the electric field vector is parallel to the strike of the discontinuities at such boundaries. A model which includes an island near a coastline is studied and contour plots as well as profiles of the electric and magnetic field component amplitudes at the surface of the Earth are given.