Abstract: Two-dimensional simulations of RM instability of an initial perturbed interface induced by shock waves are performed by using Navier-Stokes equations. The effect of initial perturbed conditions on the perturbation growth of the interface before and after the passages of reshock waves is analyzed. The computational results are compared with the predicted results by some theoretical and empirical models. It can be found that the growth rate of a single-mode initial-perturbed interface is directly influenced by the initial amplitude a₀ and wavelength λ before and after the passages of reshock waves. The growth rate of a multi-mode random perturbed interface is similar with that of the large scale wavelength of a single-mode and is also depend on the amplitude and wavelength of the initial perturbation, but the dependency is weaker than that in single-mode cases.