The scattering, and hence attenuation, of plane dilatational and shear waves due to random orientation of the grains is calculated on the assumptions that (1) the wavelength is large compared to the grain size and (2) the variations in elastic moduli from grain to grain are small compared to the average values of these moduli for the bulk material. Previous treatments of this problem are incomplete; for incident dilatational waves they are valid for a fluid (rigidity modulus=0), and for incident shear waves they describe inadequately the angular dependence of the intensity of the scattered shear waves. It is shown in this paper that for both of these types of incident waves both the scattered dilatational and shear waves are produced; the energy carried away from the incident beam by the latter is32(Vl/Vs)5times that by the former. HereVlandVsare the velocities of the dilatational and shear waves, respectively. The agreement between the theoretical and observed values of the attenuation coefficient is much better than that previously obtained by Mason and McSkimin.The attenuation due to local fluctuations in the density of a medium caused by thermal agitation is also calculated. For solids and liquids this effect is completely negligible. However, for a gas near its critical point, this attenuation is appreciable and rises sharply as the critical point is approached.