Free vibrations and buckling under uniform external pressure of thin elastic circular cylindrical shells are studied in assumption that the shell material is generally anisotropic and described by 21 elastic moduli. Non-classical equations based on the generalized Timoshenko-Reissner hypotheses are applied for the analysis of shell vibrations and buckling. The natural frequencies, the critical external pressure and the vibration and buckling modes are obtained by means of asymptotic method. As an example of the general anisotropy, a composite structure consisting of a matrix reinforced by the system of fibers inclined to the midsurface is considered. The asymptotic and numerical results of the vibration problem converge.