Configurations of shock wave reflection in steady supersonic flows have been experimentally investigated using a combination of two wedges. It has been experimentally proved by a symmetric arrangement that both regular and Mach reflections are possible in the dual-solution domain for various aspect ratio models. In the arrangement for the purpose of clarifying the influence of the wedge three-dimensionality, the transition from regular to Mach reflection can happen at any inlet aspect ratio, both when the inlet aspect ratio is increased and when it is reduced. The inlet aspect ratio has no effect on the transition provided it is high enough for the regular reflection point at the spanwise centre to be free from information from wedge edges. Flow visualization data produced using the vapour screen technique indicate that, in a region influenced by information from wedge edges, the three-dimensionality of experimental models promotes regular reflection rather than Mach reflection. To study the criteria for the transition between regular and Mach reflections, an asymmetric arrangement of two wedges has been used, and a hysteresis effect is clearly evident. The transition from regular to Mach reflection, however, occurs significantly below the detachment condition, and moreover, the repeatability of the transition angle is not satisfactorily achieved. These experimental results imply that wind tunnel disturbances may dominate the transition in the dual-solution domain. The stability of regular reflection in the dual-solution domain is discussed, and effects of free-stream disturbances are experimentally examined by producing water vapour in the free stream as an artificial disturbance.