Multi-moded horn antennas are now being proposed for far-IR space imaging systems in which diffraction limited resolution is not required (e.g. the High-Frequency Instrument (HFI) on the ESA PLANCK Surveyor). In such systems individual modes in the waveguide filter section feeding the horn can couple independently to an overmoded detector (such as a bolometer in an integrating cavity), The number of modes is chosen to optimize the coupling efficiency to the source without compromising any spillover losses. We consider in detail the case of a cylindrically symmetric corrugated configuration, presenting two alternative techniques for modelling such few-moded systems. The first approach is based on a mode-matching description of propagation in a non-uniform waveguide structure, while the second approach makes use of hybrid mode solutions for a waveguide with corrugated walls assuming a uniform but non-isotropic impedance. We present practical examples comparing the radiation patterns predicted by both models. (C) 2001 Elsevier Science B.V. All rights reserved.