This document discusses different types of axisymmetric shock wave reflections that can occur, including external and internal conical Mach reflections. It introduces the ray-shock theory used to model such reflections and presents the basic equations. It then examines specific geometries where reflections may take place, such as between a simple cone, cylinder-to-cone, and cone-to-cone configurations. The document also validates external cone reflections and models Mach reflections within conical contractions, comparing computational fluid dynamics results to predictions of the ray-shock theory.