This research work addresses questions on the vibration characteristics of single-walled carbon nanotubes (SWCNTs) using multi-scale analysis. Atomistic finite element method (AFEM) is one such multi-scale technique where sequential mode is used to transfer information between two length scales to model and simulate the nanostructures at continuum level. This method is used to investigate the vibration characteristics of SWCNTs. Open- and capped-end armchair and zigzag nanotubes are considered with clamped-free and clamped–clamped boundary conditions. The dependence of vibration characteristic of SWCNTs on their length, diameter and atomic structure is also demonstrated. The body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two carbon atoms. Based on the TB potential, a new set of force constant parameters is established for carbon nanotubes and presented in this paper. Molecular and structural mechanics analogy is used to find the equivalent geometric and elastic properties of the space frame element to represent the carbon–carbon bond. To validate the vibration results of AFEM incorporating the proposed new set of force constants, molecular dynamics simulation is also carried out on the same structure of carbon nanotube, and it is found that they are in good agreement with each other.