Abstarct: In this thesis, the mathematical solution of equations governing the nonlinear vibrations of an axisymmetric annular hyperelastic plate with moderately large deformation under transvers load has been investigated. To describe the nonlinear geometrical behavior caused by moderately large deformation in the transverse direction,Green’s strain tensor has been used, and the Mooney-Rivlin hyperelastic materials model has been used to define the material nonlinear behavior.The equations have been derived using the shear deformation theory and Hamilton's principle. The governing equations consist of three coupled nonlinear partial differential equations with variable coefficients. The perturbation theory is employed for frequency analysis and obtaining the response. To validate the results, the problem has been solved for the elastic case too. The effect of geometric parameters, material and different boundary conditions on frequency and response hve been studied. Also, the influence of transverse and radial amplitudes on the nonlinear to linear frequency ratio has been investigated. The results indicate that, in addition the transverse frequency, the radial frequency also affects on the nonlinear frequency. Also, by increasing the model constants and , the dimensionless transverse frequency for simply-simply supported and clamped- clamped annular plates ,respectively decreases and increases.