Abstract: A multi-fluid parabolic piecewise method (MFPPM) is developed to simulation of the interface instabilities in this paper. To verification and validation our code MFPPM, one experiment model from Lawrence Livermore National Laboratory (LLNL) is simulated by MFPPM, the numerical results of the gelatin-ring excellent agreement with that experiment and simulation by CALE. At the same time, the two experiment models from our Laboratory for Shock Wave and Detonation Physics are given, in which the outer and the inner surfaces of the gelatin-ring are set by mode numbers 10, amplitude 1mm in top-top and top-bottom initially. Shape, position and acceleration of the outer and the inner surfaces of the gelatin-ring simulation results are presented, and the basic physics phenomena and numerical images are excellent consistent each other.