The pressure scattered by slender bodies of revolution irradiated by a plane wave at ‘‘beam aspect’’ is formulated in a manner which relaxes the assumptions underlying the Kirchhoff analysis. While the latter stipulates that area elements scatter as though located in planar baffles, the present theory assumes that the baffles are cylindrical, i.e., that one rather than two radii of curvature is infinite. The theory gives good results in the resonance and Rayleigh regions as well as in the short-wavelength limit even for bodies whose aspect ratio is only two.