An electrostatically induced resonance behaviour of individual topological insulator Bi2Se3 nanoribbons grown by a catalyst free vapour-solid synthesis was studied in situ by scanning electron microscopy. It was demonstrated that the relation between the resonant frequencies of vibrations in orthogonal planes can be applied to distinguish the nanoribbons with rectangular cross-sections from the nanoribbons having step-like morphology (terraces). The average Young's modulus of the Bi2Se3 nanoribbons with rectangular cross-sections was found to be 44 ± 4 GPa.