The compactly supported radial basis functions (RBFs) is modified and used to the wave propagation in the anisotropic materials. An example to simulate the wave propagation in composite material is used in the paper to verify this method. In this example, stress wave propagation histories are obtained. The comparison between results by this method and by finite element method is also made. And the agreement with two results shows that this method can be used to simulate the wave propagation history in anisotropic material efficiently.