The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach Reflection (MR) and Regular Reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the x-direction with a velocity, V(t) at a free-stream Mach number of. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. Further, the Arbitrary Lagrangian-Eulerian (ALE) technique is applied to deform the mesh during the wedge motion. The dynamic transition from MR to RR is defined by two criteria, the sonic and the Von-Neumann. Moreover, the lag in the dynamic transition from the steady-state condition is studied using various reduced frequencies, κ, in the range of [0.1–2]. The lag effect in the shock system is remarkable at the high values of the reduced frequency, κ = 1.5 and 2.0. Furthermore, because the shock is bent upstream during the fast motion of the wedge, the transition from MR to RR happens below the Dual Solution Domain (DSD).