In this study, the shock wave focusing of an elliptic reflector is numerically simulated by solving the Euler equations. The numerical method is the second order upwind TVD scheme with a finite volume discretization. For the verification of the present method, we simulate the moving shock wave passing through a two-dimensional corner. The computed isopycnics are compared with the earlier experiment. Numerical results of the elliptic reflectors show that the density and pressure at the focusing point increase linearly as the aspect ratio of the reflector becomes deep. On the other hand, the gas dynamic focal length decreased with the increase of the reflector aspect ratio.