Knowledge of mechanical properties of a composite material is prerequisite to good engineering design. The problem of theoretically predicting the mechanical properties of a composite material as a function of the properties of its constituents has been thoroughly investigated by many authors [1–2]. In one general class of techniques, termed “effective modulus” theories, the composite is viewed as a homogeneous anisotropic material with “effective” elastic constants that are determined by the elastic constants of the constituent materials. All of these theories remove the microstructure of the composite from consideration and, as a result, cannot be expected to predict accurately the properties of the composite material over a wide range of deformation scales. One limitation which comes about from this “smearing” of the microstructure into a homogeneous continuum is that the effective modulus theories, and hence materials which are assumed to have “effective elastic constants”, are incapable of predicting frequency dispersion of waves, which is sometimes very pronounced in composite materials [3].