Experimental studies of CNT mechanical properties demonstrate discrepancies with analytical predictions. Since the atomic structure of carbon nanotubes demonstrates evidently anisotropic mechanical properties an analytical molecular structural mechanics model is introduced in order to derive longitudinal and circumferential moduli of nanotubes. The identification is based on the eigenfrequencies analysis of the proposed computational model. It is combined with the FE analysis and the interatomic potentials (Tersoff-Brenner and Morse). For simply supported cylindrical shells made of a specially orthotropic material the eigenfrequencies can be easily derived in the analytical way using the Rayleigh-Ritz method as the roots of the third order algebraic equations. Detailed derivations are presented and the predicted results are shown and discussed with a few computational examples.