Based on the 2-D Navier-Stokes equations, the shock induced interfacial instabilities of heterogeneous gases was simulated numerically With the finite differential method. After carrying out the comparison between numerical and experimental results, the unsteady and nonlinear characteristics of the flow field was analyzed. From the results, it is observed that the unsteady flow field of numerical simulation is similar to referenced experimentation and CFD results, and the evolvement of sulphur hexafluoride interface and the complicated wave structures are captured from simulation.