We present results of semi-empirical lattice dynamics calculations of the sound velocities in solid hydrogen under pressure based on the many-body intermolecular potential and first-principle density-functional theory (DFT). Both the sound velocities and elastic moduli are in excellent agreement with data from Brillouin scattering measurements while Silvera - Goldman and Hemley - Silvera - Goldman potentials tend to overestimate the sound velocity. It is shown that the stiffer is the potential the greater is overestimated the sound velocity. As was the case for equation of state and Raman-active lattice phonon calculations, the employed many-body potential works well for phases I and II (up to ~ 140 GPa while for higher pressures the use of the DFT is preferable.

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