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This article establishes the vibrational behavior of functionally graded plates embedded in a viscoelastic medium. The quasi-3D elasticity equations are used for this purpose. The three-parameter Visco-Winkler-Pasternak model is employed to give the interaction between the viscoelastic foundation and the presented plate. Hamilton’s principle is applied to derive the governing dynamic equations. Many validation examples are presented. Additional benchmark results are tabulated for future comparisons. The effects of various parameters like geometrical, material properties, and viscoelastic foundations on the vibrational frequencies of homogeneous and functionally graded plates are investigated. The frequencies increase as all parameters increase except the functionally graded power-law index for which its increase causes a decrease in the frequency value.