Abstract: The nonlinear governing equations of composite laminated plates with edges elastically supported against rotation are established by the generalized Fourier series method. The influence of the inhomogeneous term of the equations is discussed. Since the inhomogeneous term contains all information of the boundary conditions, the applied load and the imperfection, it can be directly used in determining whether buckling will happen in the laminated plates. The causation to produce prebuckling coupling deflection is clarified in mathematics. The uniqueness of the prebuckling solution is proved with the matrix theory and the nonlinear functional knowledge, and the general way to solve the nonlinear stability problem of composite laminates is brought forward.