We report on the direct observation of confined acoustic phonons in the photoluminescence spectra of single CdSe-CdS-ZnS nanocrystals, whose ligands were exchanged to poly(ethylene oxide) (PEO) before they were embedded in a PEO matrix. Modeling a nanocrystal as an elastic sphere, the confined acoustic modes can be assigned to purely radial vibrations: the breathing mode and its two first radial harmonics. In addition to acoustic modes, we also observe longitudinal optical modes of the core material and, remarkably, also of both shell materials.