Based on the wave propagation algorithm, a numerical scheme of multi-component reactive system is constructed. The interaction between the incident shock wave and the flame bubble, and between the reflected shock wave and distorted flame of the CH₄/air mixture are investigated numerically in the Cl₄/air elementary reaction model and the splitting method. The evolution and properties of the flame instability induced by incident and reflected shock waves are discussed. The computation indicates that the Helmholtz instability, Richtmyer-Meshkov instability and chemical heat release rate play important roles in the interaction between shock waves and the flame. The calculated results are compared with experimental ones, and an agreement is shown.