The unsteady supersonic jet formed by the shock tube with small high-pressure chamber was used as a simple alternative model of Pulsed laser ablation. Since the pressure of the shock wave formed by Pulsed laser ablation is very high, the interaction between the shock wave and the plume is important for the formation of nanoparticles especially under high background gas pressure. An elliptical cell is used for controlling the shock wave. The shock wave discharged in one focal point converge another focal point. Numerical calculation was carried out by solving the axisymmetric two-dimensional compressible Navier-Stokes equations. The wall static pressure monitored at the center of substrate is used to evaluate the influence of the shape and the pressure ratio on the behavior of the shock wave, the plume, and their interaction. As a result, it was found that the vortex ring was generated downstream of the cell, which is followed by the discharging shock wave from the cell exit. It was also found that the influence of the vortex ring on the wall static pressure at the center of the substrate.