A successive approximation method proposed and applied in connection with static and dynamic analyses of homogeneous isotropic, orthotropic and cross-ply laminated hollow cylinders and cylindrical panels(1-6) is outlined and its applicability is extended in connection with corresponding thermoelastic analyses. Nevertheless, the method is further applied in connection with the buckling problem of simply supported hollow cylinders and cylindrical panels subjected to certain external mechanical loadings. To deal with finite cylinders subjected to more complicated loading that simply supported edge conditions, an approach is outlined which is suitable for corresponding analyses of hollow cylinders having fixed edge boundaries.