The mathematical description of damped vibrations of laminated polymer quasihomogeneous plates is suggested on the basis of the variation Hamilton principle, corrected Mindlin plate's theory and the elastic-viscoelastic correspondence principle in the linear theory of viscoelasticity. The mathematical description of damped vibrations of taminated polymer quasihomogeneous plates is proposed. The elastic eigenvalue problem is solved on the basis of the Ritz's method. Iteration method of the third precision order is used to find the frequency equation's complex roots for damped vibrations problem. The convergence and reliability estimations of the elaborated mathematical description are shown.