In this paper, nonlinear equations of motion for laminated composite rectangular plates based on the first order shear deformation theory were derived. Using a perturbation method, the nonlinear equation of motion was solved and analytical relations were obtained for natural and nonlinear frequencies. After proving the validity of the obtained analytical relations, as an alternative and simple modeling technique, ANN was also employed to model the laminated rectangular plates and predict effects of different parameters on the natural and nonlinear frequencies of the plates. In this respect, an optimal ANN was selected and trained by training data sets obtained from analytical method and also tested by testing data sets. The obtained results were in good agreement with the analytical and published results.