Silver films on a glass substrate with a thickness range of 34-900 nm were examined using Brillouin spectroscopy. The surface plasmon resonance was used to determine the thickness of the thinner films very accurately and to enhance the Brillouin signal. With a special scattering setup. the Rayleigh and first Sezawa mode could be observed over a Aide wavevector range. From the two dispersion branches, the elastic constants c(ij) were detetmined. assuming a hexagonal symmetry. It transpired that the mechanical properties of the films were dependent on film thickness. The elastic constant c(44) shows a systematic behavior-starting nearly from the isotropic value. it decreases with decreasing film thickness. The hexagonal model works well for films thicker than 60 nm and the lowered value for c(44) can be satisfactorily explained by a preferred [111] orientation of the silver crystallites. However. for the thinnest films, the crystallite orientation cannot explain the strong decrease solely in c(44). Other effects, like surface roughness, become important.