This paper aims to study sound wave propagation in individual multiwall carbon nanotubes based on a multiple-elastic beam model. The present model predicts that there exist (N-1) critical frequencies (within terahertz range) for an N-wall carbon nanotube. Sound wave propagation in multiwall carbon nanotubes is almost coaxial only when the frequency is much below all critical frequencies, and becomes substantially non-coaxial when the frequency is higher than at least one of the (N-1) critical frequencies. In the latter case, the sound speeds predicted by the present model are significantly higher or lower than that given by the existing single-beam model. Hence, terahertz sound waves in multiwall carbon nanotubes exhibit complex new phenomena and are essentially non-coaxial.