The acoustic vibrations of metal nanoparticles encapsulated in a dielectric shell (Ag@SiO(2)) were investigated using a time-resolved femtosecond technique. The measured vibration periods significantly differ from those predicted for the bare metal cores and, depending on the relative core and shell sizes, were found to be either larger or smaller than them. These results show that the vibration of the whole core-shell particle is excited and detected. Moreover, vibrational periods are in excellent agreement with the predictions of a model based on continuum thermoelasticity. However, such agreement is obtained only if a good mechanical contact of the metal and dielectric parts of the core-shell particle is assumed, providing a unique way to probe this contact in multimaterial or hybrid nano-objects.