A closed form solution is obtained to describe, in a physically appealing manner, the reflection and diffraction of a general astigmatic Gaussian beam which is incident on an arbitrary smooth, electrically large, slowly varying curved, perfectly conducting screen (or reflector). This closed form solution is obtained via an asymptotic evaluation of the radiation integral for the fields scattered from the reflector, to within the physical optics approximation that remains valid for the present situation. The analysis developed here is particularly well suited for the fast analysis of electrically large reflector antennas by representing the feed illumination by a relatively small set of Gaussian beams launched from the feed plane. Each of these Gaussian beams after being launched undergoes reflection and diffraction at the reflector; the expressions for the reflected and diffracted fields are developed in this paper and utilized by Chou <1996> to compute the radiation pattern of large reflector antennas in a matter of a few seconds as compared to the conventional numerical physical optics integral method which takes hours on the same computer.¿ 1997 American Geophysical Union