The prblem of a cylindrical feed radiating in the presence of an axisymmetric reflector is formulated in terms of a combined electric and magnetic field integral equation. This equation is simplified by means of an optical approximation and numerical solutions are obtained using the method of moments. The field radiated by the combination of feed and reflector is computed using a hybrid physical optics and moment method approach, where the effects of feed-reflector coupling are taken into account. Examples are given of the method applied to the analysis of a splash-plate feed and a dual-mode coaxial feed illuminating a paraboloidal reflector.