A mathematically accurate and numerically efficient method of analysis of a spherical reflector, fed by a scalar beam produced by a complex source- point feed, is presented. Two cases, soft and hard reflector surface, are considered. In each case the solution of the full-wave integral equation is reduced to dual series equations and then further to a regularized infinite- matrix equation. The latter procedure is based on the analytical inversion of the static part of the problem. Sample numerical results for 50-λ reflectors demonstrate features that escape a high-frequency asymptotic analysis. (C) 2000 Acoustical Society of America.