Susceptibility to fracture of materials due to vibration is determined from the stress and frequency. Maximum amplitude of vibration must be within the limits for the safety of the structure. Hence vibration analysis has become very important in designing a structure. The solution to nonlinear or large amplitude vibration of low flexural rigidity structures as obtained based on the lineage models provides no more than a first approximation to the actual solutions. The increasing demand for more realistic models to predict the responses of elastic bodies combined with the availability of super computational facilities have enabled researchers to abandon the linear theories in favour of non-linear methods of solutions. In the present investigation, large amplitude vibration of several rectangular plates has been studied using the finite element method. The formulations have incorporated the shear deformation of the plates. Effects of variations in the Poisson''s ratio, thickness parameter & plate aspect ratio on the non-linear frequency ratio has been included in the research. This book is meant for scholars who are beginners in the study of FE analysis of vibrational responses.