In this paper, the phonon spectra of infinite length single-wall carbon nanotubes are calculated based on the force constant model. The dependence of specific heat on the tube diameter and temperature is discussed. It is found that the specific heat will increase with increasing temperature and In this paper, the phonon spectra of infinite length single-wall carbon nanotubes are calculated based on the force constant model. The dependence of specific heat on the tube diameter and temperature is discussed. It is found that the specific heat will increase with increasing temperature and diameter and approaches to a constant value. Also, the vibrational spectra of the finite length （5,5） carbon nanotube are calculated. The relationships between the vibrational frequency and length are presented for some particularly modes.diameter and approaches to a constant value. Also, the vibrational spectra of the finite length （5,5） carbon