An integral equation method is used to formulate the problem of scattering by rotationally symmetric horn antennas. The excitation is assumed to be due to an infinitesimal dipole antenna, while the secondary field is obtained by assuming anisotropic impedance boundary conditions on the horn surface. This formulation is then used to investigate numerically the radiation from corrugated conical horns by approximating the corrugated surface with anisotropic surface impedances. The method is also used to study the scattering properties of receiver horns. In this case the external load is simulated by an impedance surface at the inner-end wall of the horn antenna, which is illuminated by an axially incident plane wave.