The effect of shells of various thicknesses on the vibrational resonant Raman spectra of CdSe/ZnS core-shell nanoparticles is studied. The dependence of the core-shell structure on the method of shell deposition is derived from a comparison of the vibrational and photoluminescence spectra of nanoparticles. Along with the appearance of peaks attributed to the shell, the phonon spectrum of the core undergoes significant changes upon shell growth. The change of the CdSe LO peak lineshape in core-shell nanoparticles is discussed with respect to possible changes in the spectrum of both optical and acoustical phonons upon shell formation. Based on the observed decrease of the CdSe 2LO/LO peak intensity ratio, a weakening of exciton coupling to the CdSe LO phonon upon ZnS shell deposition is supposed. The change in the carrier localization volumes upon shell formation is discussed as a possible reason for the reduced coupling.