This paper deals with the problem of dynamic stability of angle-ply laminated cylindrical shells subjected to static and periodic axial compressive loading. First, the axially symmetric motion of the shell under loading is determined. Subsequently, certain perturbations are superimposed on this motion, and their behavior in time is investigated. The symmetric state of motion of the shell is called stable if the perturbations remain bounded. The solutions for the prebuckling motion and the perturbated motion are obtained by the use of Galerkin's method. Stability regions are examined by utilizing Mathieu's equation. The inevitability of dynamically unstable behavior is proved analytically and the effects of various factors, such as fundamental natural frequency, vibrated amplitude and dynamic unstable mode, are clarified.