Raman scattering has been used to study a variety of InSb/In1-xAlxSb strained-layer superlattices grown by magnetron sputter epitaxy. The observed frequencies of zone-folded longitudinal acoustic phonons agree well with those calculated using Rytov's theory of acoustic vibrations in layered media. The intensities of these phonons do not coincide with those calculated within the regime of the photoelastic mechanism for light scattering because the exciting light energy is close to resonance with superlattice electronic transitions. The longitudinal optic phonons in In1-xAlxSb layers exhibit two-mode behavior and their shift due to the intralayer strain is discussed.