Abstract: Wave impeding block (WIB) vibration isolation system as an effective measure for vibration pollution control is applied in practical engineering gradually, but the previous studies mostly focused on the single-phase solid homogenous materials, few research have been on the vibration isolation performance of wave impeding block with materials properties that have a continuous variation along space relatively. Based on the functionally graded material, a new type of foundation vibration isolation system is proposed. Considering setting the graded wave impeding block in the elastic foundation which subjected to surface strip harmonic load, using the Fourier transform and Helmholtz vector decomposition, the calculation formula of reverberation ray matrix method (RRMM) is established for two-dimensional transient response of elastic foundation based on the line elastic theory. Assuming that the material properties of graded wave impeding block have an exponential law distribution along the thickness-coordinate, by using numerical inverse Fourier transformation, the displacement and the stress are obtained. Via numerical examples, the effectiveness of vibration isolation of graded wave impeding block is compared to conventional single phase solid homogenous wave impeding block, and the influences of physical and mechanical parameters including the gradient factor, the depth and the thickness of graded wave impeding block are analyzed. The results show that the graded wave impeding block can effectively reduce the vibration amplitude, and compared with the single phase solid homogenous wave impeding block isolation system, graded wave impeding block isolation system has better effect. The amplitude of displacement and stress is decreased with the increase of gradient factor. The effect of vibration isolation of graded wave impeding block improved with the increased of the thickness, but reduced with the increasing of the embedded depths.