An expression for the attenuation of a generalized Rayleigh wave has been obtained in terms of a viscosity tensor. The values of the viscosity components for Quartz obtained from measurements on bulk waves have been used to calculate the attenuation of several surface waves on that material. An attenuation of 7.0 dB/cm is predicted at 1 GHz and 300°K for the surface wave propagating in theXdirection on theYsurface. This figure compares favorably with an experimental value of 8.6 dB/cm at the same temperature and frequency. An expression for the attenuation of Rayleigh waves on isotropic media is also discussed.