The multilevel fast multipole algorithm (MLFMA) is extended to the problem of an arbitrarily shaped dielectric target in the presence of a lossy, dispersive half-space. The near MLFMA terms are treated rigorously, via a complex-image-technique-based evaluation of the Sommerfeld integrals inherent to the half-space Green's function. The Green's function components for the far MLFMA terms are evaluated approximately, but accurately, via an asymptotic analysis. In this paper, we detail the scattering formulation and perform a comparison of MLFMA-generated results with those from other, simpler (and less general) models. ¿ 2001 American Geophysical Union