Abstract: An investigation into unsteady shock wave reflections over three-dimensional intersecting wedges is described. The finite volume method with the MUSCL-Hancock interpretation is used on self-adaptive unstructured meshes. Numerical results demonstrate that three-dimensional Mach reflection region predicted by the relations of two-dimensional oblique shock wave reflection has limitations because of the three-dimensional effect of shock reflections. An atypical three-dimensional structure appears in this region, namely the second type of three-dimensional Mach stem. Besides, for different combinations of shock wave Mach numbers and wedge angles, the three-dimensional four-shock Mach reflections or three-shock regular reflections appear in the corner of the two intersecting wedges.