The paper deals with the problem on the connection of mechanical and optical properties of silicon and germanium nanoparticles. Experimental evidence of insignificant influence of nanoparticle sizes on oscillatory motions of lattice ions of medium is considered. In particular, the experimental results obtained by thermoluminescent methods and the excitation of acoustic vibrations by light in nanoparticles and macroenvironment are examined. It is shown that the theory of elasticity can be applied to describe the vibrations of nanoparticles. Using the equations of elasticity theory, the values of radial eigen frequencies of vibrations for the spherical silicon and germanium nanoparticles are calculated. The optical properties of such nanoparticles and the possibility of their modulation by elastic oscillations are considered. The applications of obtained results to the design of sensor systems (for the detecting of medium oscillations in the kilohertz frequency range) as well as for the use in information technologies are examined.