<p>Bi-stable variable stiffness (VS) structures are passive systems that can maintain equilibrium after shape changes, making them a promising approach for adaptive structures. In this paper, a simple analytical model based on the Rayleigh–Ritz method is used for static and dynamic analysis of square and rectangular unsymmetrical bi-stable VS composite laminated plates, and Hamilton’s principle is used to investigate the dynamic snap-through phenomena. The effects of ply thickness, ply angles, and aspect ratio on strain energy and out-of-plane displacements of two stable states and dynamic snap-through are investigated. Also, the obtained analytical results are compared with finite element analysis to validate the accuracy of model. The obtained results show a good agreement between the analytical and finite element method, and show the good efficiency of the present method for use in VS composite structures.</p>