We derive an extended Born approximation for electromagnetic scattering due to rock formations that exhibit axial symmetry around a well bore. An alternative formulation is also developed to improve the accuracy of the approximation when scattering takes place in close proximity with the source. The resulting equations are solved via a numerical procedure that is as efficient as the first-order Born approximation but substantially more accurate. This conclusion follows from studies carried out on a variety of source-receiver configurations and frequencies typical of single-well induction measurements. ¿ 2001 American Geophysical Union