As a normal shock wave moves through a convergent tunnel, its strength and structure change, which was discussed in details by Whitham who proposed “Ray Shock Theory”. Due to rare numerical schemes for capturing shock waves, extremely less numerical simulations have been carried out to study this phenomenon to date. With the development of numerical schemes, TVD (Total Variation Diminishing) scheme was proposed for capturing complex shock systems. In the present studies, numerical studies were performed to investigate moving shock waves across convergent tunnels and compared with theoretical calculations. TVD scheme was used to calculate both inviscid and viscous unsteady flows with moving shock waves. Different Mach numbers of normal shock waves induced by a shock tube at different diaphragm pressure ratios were discussed. The detailed Mach number of a shock wave varying with the area change of the convergent section was obtained as well as the change of the structure of the shock wave in the convergent section.