A multipole expansion technqiue is developed for calculating the co-polar and cross-polar radiation patterns of a prime-focus paraboloid fed by a dominant-mode rectangular waveguide feed. Initially, the feed radiation pattern is expressed in terms of electric and magnetic multipoles of different orders which are subsequently used to obtain the secondary radiation patterns (co-polar and cross-polar) in explicit closed form in the form of a rapid by a converging algebraic series. The validity of the analysis is effectively demonstrated by calculating the co-polar and cross-polar patterns of a typical paraboloid and comparing and results with calculations based on the direct numerical integration of the physical optics currents induced on the reflector surface. Copyright © 1980 by The Institute of Electrical and Electronics Engineers, Inc.