In the paper, propagation of two-dimensional viscous-plastic waves in graded layer media is investigated by numerical method. Firstly, an infinite model is used to analysis wave’s propagation in FGMs, this model has a finite gradient layer and non-reflecting boundary condition is used to simplify the model to be finite. Then the characteristic of viscous-plastic wave’s propagation in graded media is investigated on the base of this model. The following contents is researched by this model: (1) The refracted effect of functionally gradient layers on incident wave; (2) the effect of incident angle on the bottom layer’s stress ; (3) the effect of gradient layer’s thickness on the bottom layer’s stress. Finally, some interesting, reasonable and important results are obtained by our researching work.