A theory is presented for determining the ensemble‐averaged Green's function of a random distribution of identical, randomly oriented elastic scatterers embedded in an infinite, homogeneous, and isotropic matrix. The average Green's function for such a medium is characterized by three parameters which are analogous to the Lame constants and density of an ideal, homogeneous, and isotropic medium. The theory can thus be thought of as having as its goal the determination of “effective” elastic parameters and density which characterize the composite medium. The theory is based on the self‐consistent formulation of Lax's multiple scattering theory [M. Lax, Phys. Rev. 85, 621 (1952)] due to Gyorffy [B. L. Gyorffy, Phys. Rev. B1, 3290 (1970)] and Korringa and Mills [J. Korringa and R. L. Mills, Phys. Rev. B5, 1654 (1972)]. Application of the quasicrystalline approximation (QCA) results in three coupled equations which must be solved jointly for the ensemble‐averaged Green's function. These equations are solved a...