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Transient solutions will be developed for laminated simply supported closed cylindrical shells subjected to a uniform dynamic pressure at the outer surface of the cylinder. These solutions are obtained by using General Third Shell Theory (G.T.T.). Rectangular pulse, triangular pulse, sinusoidal ulse and (ramp-constant) load-time varying functions are studied and the required equilibrium equations are developed. The central deformation and principle stresses are investigated for different cross-ply laminates.