The electromagnetic characterization of one or more conductive obstacles buried in a conductive subsoil from low-frequency data (induction regime) is expected to benefit from a fast yet fairly accurate solution of the direct problem associated to it. Here, an approximate model is proposed to that effect. It is based on the localized nonlinear approximation, coupling between obstacles (whenever two or more) being approached via the Lax-Foldy theory of multiple diffraction. The obstacles are modeled as generic ellipsoids, with spheres as the limit case. The exact primary field due to an electrical loop (or a magnetic dipole) is calculated, and its low-frequency expansion is introduced. A semianalytical solution of the direct problem is developed from the exact field formulation, analytical solutions being proposed in the most simple cases of either sources or configurations. The model is validated by comparison with numerical experimentations carried out by tools available from the CIVA platform and by the FEKO code. Limits of the model are explored also, notably about the retrieval of the pertinent geometric and electric parameters of an ellipsoid buried in a half-space from sparse data collected above it.