Today, composite materials have many applications in various industries. A justify; LINE-HEIGHT: normal; TEXT-INDENT: 17.85pt; MARGIN: 0in 0in 0pt" In this thesis, different statical, thermal and vibratory behaviors of multistable morphing composite plates with regard to the bending - membrane behavior coupling are analyzed. For this purpose, the principle of minimizing the potential energy and Rayleigh–Ritz approach are used. In the method presented in this thesis, at first, the membrane and the bending components of the total strain energy are decoupled using the semi-inverse formulation of the constitutive equations. Then, in order to increase the accuracy of the results, the membrane problem is solved by combining compatibility conditions and using the Differential Quadrature Method (DQM) and numerical method. Differential quadrature method in comparison to the low level methods provides accurate results at a relatively small computational cost. Also, transverse displacements are approximated using Legendre polynomials. In order to validate and demonstrate the high accuracy of the proposed method compared to Hyer method, equilibrium and stable states and the force required to snap through between these states for a bistable composite plate with initial flat state are found. The advantage of the method used in this thesis is prediction the different behaviors of bistable composed plates with initial curvature and various boundary conditions. In the following, stable states of a bistable composite plate with the initial curvature and a bistable composite plate with fixed point edge boundary condition are found. The effect of changing side length, aspect ratio and temperature change on stability region and out of plane displacement of bistable composite plate with the initial curvature are obtained. Further, a new type of bistable twisting hybrid composite plate with an external metal layer is discussed. Due to difference between the deformation of this type of bistable composite plates and deformation of other types, a comparison between their various behaviors has been done. In next step, small amplitude vibration around the equilibrium states is investigated. For this purpose, the perturbation term is added to the coefficients of displacement fields and the governing equations are determined using Hamilton's principle. Solving the governing equations, the natural frequencies and mode shapes for different stable states of various bistable composite plates are determined. Also, effect of adding a metal layer on the smallest natural frequency of bistable composite plate and the mode shape associated to it is investigated. To validate the results, finite element analysis using ABAQUS software has been done and also the results are compared with the results of other works which have been done by other researchers. Keywords: Multistable structures, Morphing structures, Differential quadrature method, Hamilton's principle, Bistable twisting hybrid composite plate, Vibration around the equilibrium state