  We study the phonon modes in single-walled MoS$_{2}$ nanotubes via the
lattice dynamics calculation and molecular dynamics simulation. The phonon
spectra for tubes of arbitrary chiralities are calculated from the dynamical
matrix constructed by the combination of an empirical potential with the
conserved helical quantum numbers $(\kappa, n)$. In particular, we show that
the frequency ($\omega$) of the radial breathing mode is inversely proportional
to the tube diameter ($d$) as $\omega=665.3/d$ {cm$^{-1}$}. The eigen vectors
of the first twenty lowest-frequency phonon modes are illustrated. Based on
these eigen vectors, we demonstrate that the radial breathing oscillation is
disturbed by phonon modes of three-fold symmetry initially, and the tube is
squashed by the modes of two-fold symmetry eventually. Our study provides
fundamental knowledge for further investigations of the thermal and mechanical
properties of the MoS$_{2}$ nanotubes.
