We predict both the surface plasmon line width and the figure of merit oscillations in metal nanoparticles with varying the dielectric constant of an embedding medium. The calculations are based on the kinetic equation approach, which allows one to account for the effects of electrons’ collisions with the nanoparticle surface in the case when the electron mean free path is much greater than the particle size. Main attention is paid to the electron-surface scattering contribution to the plasmon decay. All calculations of both the line width and the figure of merit are illustrated by the example of the Au and Na nanoparticles with different radii.