Numerous applications of plate structures may be found in aerospace and marine engineering. The present study is a continuation of the work by Amabili and Sirwan [1] extending their investigation to laminate composite rectangular plates with different boundary conditions subjected to an external point force. The excitation frequency lies within the neighbourhood of the fundamental mode of the plate. The analysis is performed using three different nonlinear plate theories, namely: i) the classical Von Kárman theory, ii) first-order shear deformation theory, and iii) third-order shear deformation theory. The plates are tested using three sets of boundary conditions: a) classical clamped boundary conditions, b) simply-supported ends with immovable edges, and c) simply-supported ends with movable boundaries. The results discuss the limitations associated with using lower order theory to describe the large-amplitude oscillations of plates, investigate the effect of boundary conditions highlighting the different responses obtained from using isotropic or laminate composite rectangular plates and indicate chaotic oscillations observed for specific values of the excitation force.