In this present paper we present a novel solution for the diffraction of a converging beam. In that approach, the field of the incident converging beam is synthesized using the CS approach in conjunction with the plane wave spectral analysis, and the diffracted field is calculated using the appropriate integral representation expansion. The exact solution obtained via this spectral technique is then compared with an asymptotic solution obtained via CR tracing augmented with uniform complex ray diffraction. The CR solution includes also selection rules that delineate the CR lit and shadow zones for the diverging or converging beam cases. The overall goal of this research is the derivation of techniques for the analysis of 3D beam diffraction by a cone.