The theory of the longitudinal vibrations of a composite ’’crystalline-amorphous’’ elastic rod with perturbing forces at the ends has been developed. The longitudinal-acoustic-mode fundamental frequencies are tabulated as a function of the relative elastic moduli, relative densities, and relative composition of the components, as well as of the magnitude of the perturbing forces. It is shown that this model can explain the behavior of the observed Raman-active low-frequency bands associated with this mode in polyethylene and in isotactic polypropylene.