Abstract: Based on three-dimensional viscoelastic constitutive relationship, a differential equation of motion for Kelvin's viscoelastic thin rectangular plate with interior elastic point supports is derived in this paper, in which a two-dimensional generized function δ appears. The complex characteristic equation for free vibration of Kelvin's viscoelastic thin rectangular plate with simple supports along all edges and additional interior point supports is obtained by the integral equation method. The effects of the dimensionless delay time of Kelvin's viscoelastic materials, the elastic constant of the elastic point supports and location of elastic point support on the natural frequencies of the plate are discussed.