The shock structures formed by the supersonic flow over three-dimensional intersecting wedges are simplified and analyzed on the two-dimensional characteristic cross section by the pseudo-steady shock wave reflection theory. Three-dimensional Euler equations are solved to validate the analytical results. Numerical results demonstrate that transitional and double Mach reflections, which could not form in two dimensional steady shock wave reflections, would form for some combinations of wedge angles and inflow Mach numbers in this steady supersonic flow. This phenomenon is analysed in this paper, and combinations of wedge angles and inflow Mach numbers for different shock wave reflection patterns are solved. Moreover, the effects of the dihedral angle of the corner and the sweep angle of the leading edges are discussed. It is found that the regular-Mach reflection transition in this problem accords with the von Neumann criterion.