Abstarct: In this research, The mathematical solution for vibration of viscoelastic circular and annular plates under radial and transverse load with various boundary conditions has been taken. Four coupled partial differential equations are obtained by using Hamilton’s principle and baxsed on first order shear deformation theory. The viscoelastic behavior is assumed standard linear solid in shear and elastic in bulk. The perturbations technique has been used for frequency analysis and transient response. By the same procedure, analysis has been performed by classical plate theory. The Numerical analysis has been done by using ANSYS FE package. Contents that are considered in this analysis are such as: Determination of response in terms of displacement and time, calculation of the natural frequencies, investigation of the geometrical parameters effect on the response and natural frequencies, suveying accuracy of the first order shear deformation theory with respect to the classical plate theory and numerical solution.