In this paper, using modified couple stress theory, a new cylindrical shell element is introduced. Here, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model which has been used in previous research, vibrational behavior and buckling behavior of nanotubes is investigated via the finite element method. In addition, the new cylindrical shell element is defined, the mass-stiffness matrix is developed, and the use of the super element and size-dependent finite element formulation together with shell element is extended to more precisely account for nanotube vibration and buckling. The new cylindrical shell element has been developed based on super element's shape function. In special cases, in order to investigate the application of the equations developed, the cylindrical nano-shell bending displacement is studied using modified couple stress cylindrical shell element and the results are validated using the analytical method. In addition, the effects of parameters such as length scale parameter, length, and thickness on cylindrical shell displacement are investigated. The results have indicated using the super element considerably reduces the amount of computations and analysis time in comparison with the use of molecular dynamic simulation.