Summary: The finite-element boundary-integral method is a powerful technique for dealing with scattering and radiation problems involving complex geometries and inhomogeneous media. The capability of the technique is limited mainly by the full matrix generated by the discretization of the boundary integrals involving Green's functions. In this paper, this limitation is lifted using the fast multipole method, which evaluates the boundary integrals at a reduced complexity. The resulting new technique is applied to the problem of electromagnetic scattering by cavity-backed apertures and microstrip antennas. Numerical results are presented to demonstrate its validity and capability.