This paper presents an analytical-numerical approach to model problems that are ubiquitous in the theory of radio wave propagation. The method is particularly efficient for considering three-dimensional diffraction by a localized perturbation of the environment. Here we are concerned with VLF and LF (less than 100 kHz) radio wave propagation in the presence of an irregularity of finite lateral extent (ionospheric disturbance or Earth's surface inhomogeneity). The surface impedance concept is used to model the Earth-ionosphere waveguide. Our approach is based on preliminary asymptotic integration of the rigorous two-dimensional integral equation in order to facilitate its further numerical handling. An original computational algorithm is proposed to invert an approximate equation. By reducing CPU time, the developed procedure enables study of both small and comparatively large irregularities. In spite of accepted asymptotic compromises, most of the three-dimensional effects that are intrinsic to similar problems are obtained during numerical simulations.¿ 1997 American Geophysical Union