Defects are ubiquitous in carbon nanotubes (CNTs), despite their large formation energies, and have astounding effects on their physicochemical properties. In this study, we employ density-functional theory (DFT) calculations to study systematically the atomic structure, stability, and characteristic vibrations of pristine and defected zigzag CNTs, where the defects are of the form of Stone Wales (SW) and diatom vacancies (DV). The DFT optimized structures and the phonon modes are subsequently used in conjunction with a semiempirical bond-polarization model to study the nonresonant Raman spectra. For each defect type, we find two CNT structures with defects parallel or oblique to the tube axis. For the SW defects, the two structures have similar formation energies, whereas for the DV defect, only defects parallel to the tube axis are likely to exist. The results show that the defects induce a blue shift in the radial breathing mode (RBM) of metallic CNTs, whereas this mode is not shifted for semiconducting CNTs. However, the RBM shift or its Raman profile is not sensitive to the defect type. The G-band showed more sensitivity to the defects in the form of a red/blue shift in the frequency, or a partial/complete defragmentation of the G bands.