The dynamics of amphiphilic films deposited on a solid surface is analysed for the case in which shear oscillations of the solid surface are excited. The two cases of surface and bulk shear waves are studied with the film exposed to a gas or to a liquid. By solving the corresponding dispersion equation and the wave equation while maintaining the energy balance, we are able to connect the surface density and the shear viscosity of a fluid amphiphilic overlayer with the experimentally accessible damping coefficient, phase velocity, dissipation factor, and resonant frequency shifts of shear waves.