Abstarct: In the present thesis, the free and forced vibrations analysis of asymmetric viscoelastic annular and sector plates with small deflection are studied using the first order shear deformation theory. The viscoelastic behavior is assumed to be the standard linear solid in shear and elastic in bulk. The boundary conditions are clamped, simple and free for free vibrations. The applied force is transverse and the boundary condition is simply supported for the forced vibration. The Hamilton’s principle was employed to derive governing equations including five coupled partial differential equations with variable coefficients. An analytical method baxsed on the perturbation technique and the Fourier series has been used to solve the governing equations. Determination of the natural frequencies, mode shapes and the response are considered. In addition, the sensitivity of the results to the geometrical and mechanical parameters is investigated. The results are compared with those obtained from the literatures and finite elements package.