Two Different schemes are examined for vibration analysis of composite plate with variable thickness resting on non-uniform and nonlinear elastic foundation problems. On the basis of first order transverse shear theory a basic equation of vibration is derived. Investigations are made over non-uniform and nonlinear Winkler and uniform Pasternak foundation model. Examined schemes are based on discrete singular convolution and moving least square differential quadrature method. Also, the obtained nonlinear algebraic system is solved by using iterative quadrature technique. This problem is solved for different boundary conditions, different shear correction factor and varying thickness in one and two directions. Numerical analysis is applied to investigate influence of different computational characteristics on convergence and accuracy of the obtained results. The obtained results agreed with the previous analytical and numerical ones. Further a parametric study is introduced to explore the influence of elastic and geometric characteristics of the vibrated plate, on results.