Abstract: Following Loves shell theory, the governing equations of the composite cylindrical shell associated with asymmetric deformation perturbance were obtained. By taking the displacement functions as complex Fourier series at the perturbed state, the perturbed motion equations were deduced to a set of Mathieu equations. Then the critical load and natural frequencies were calculated. Previous studies on dynamic stability of laminated shells had not taken into account the geometric nonlinearity which was considered in the present work. Numerical results showed that the critical load yielded by geometric nonlinearity was about 5 % higher than that given by geometric linearity.