Abstract: The present paper analyzes the vibration of simply supported plates of functionally graded materials resting on viscoelastic foundations. Based on the Reddy's higher-order shear deformable plate theory and the general Karman-type equations derived by Shen, the analytical solutions for the free vibration and the transient response are obtained by using the double Fourier series. The natural frequencies and the transient response are obtained, and the results are compared with those of other papers. The effects of the volume fraction index, the parameters of the viscoelastic foundations and the ratio of the length to the thickness are analyzed. The results show that the natural frequencies rise, but the transient responses decrease with the increase of the pressed and sheared parameters of the viscoelastic foundations, and the viscous parameter also has an effect on the natural frequencies and the transient response.