The vibrational structures of trans- (TAB) and cis-azobenzene (CAB) are of interest due to their importance in optoelectronic applications as well as due to the unique isomerization mechanism involving the inversion process (at the nitrogen site). In this paper, we report the equilibrium structures, harmonic frequencies, and mode assignments for TAB and CAB and their isotopic analogues, using restricted Hartree-Fock (RHF), hybrid Hartree-Fock/density functional (HF/DF), and pure density functional theoretical (DFT) methods utilizing the 6-31G* basis set. The results of the optimized molecular structure obtained on the basis of RHF and all the DFT calculations are presented and then critically compared with the experimental electron diffraction results. It is observed that best structural parameters are predicted by the hybrid HF/DF method, viz. B3LYP and B3P86 followed by the pure DFT method BP86. In the case of harmonic vibrational frequencies (unsealed) and the normal modes, it is found that the BP86/6-31G* is the most accurate. The data obtained here has been used to reassign (in contrast to the previously reported MP2 results) some of the vibrational frequencies, particularly, for the main N=N and C-N vibrations of TAB. On the basis of BP86/6-31G* force field, the infrared intensities for both TAB and CAB and their isotopomers have also been calculated. Moreover, the main differences in the vibrational spectra of the two isomers of azobenzene have been discussed from normal mode analysis.