In this thesis, the elastic wave propagation in discrete random media is studied to predicted effective dynamic properties of inhomogeneous materials including fiber-reinforced and particulate composites. Two different formalisms of multiple scattering are suggested for identification of the dynamic characteristics of dense scatterer systems. Firstly, the exact pair-correlation function is incorporated with the classical multiple scattering theory. The contribution of doubly scattered waves to total field as a first significant correction to the single scattering approximation is considered approximately by using the pair-correlation function. The pair-correlation functions for various volume fractions are obtained by using the Monte Carlo simulations developed in statistical mechanics. Consequently, the unphysical results of negative attenuation usually predicted by the ordinary quasicrystalline approximation ignoring the pair-correlation between scatterers can be overcome. Secondly, the self-consistent coherent potential approximation used only in static problem is expanded to dynamic one. Three conditions that must be satisfied by two effective elastic moduli and effective density are derived without limit of frequency for the first time. The frequency-dependent complex effective properties can be obtained numerically by solving the derived self-consistency conditions. Dynamic characteristics of several composite materials are obtained by solving the dispersion relations found from the former and latter theories. Boron/Alumium FRC shows very weak dispersion because there is no notable resonance of scatterers in calculation frequency range. The dispersion and attenuation of SH wave are strongest than other wave modes in FRC. The relative importance between the matrix viscoelasticity and the multiple scattering is compared for Boron/Epoxy FRC. In this material, the viscoelasticity of matrix affect on the dispersion and attenuation up to k$_l^1\alpha\approx 1$, because the resonance of scatterer is not so intense. Therefore, it can be concluded that the inclusion of the effect of viscoelasticity in multiple scattering formulation is very significant in obtaining the dynamic characteristics of various composite materials fabricated in viscoelastic matrices. From the resultant spectra of the effective properties of Lead/Epoxy particulate composite obtained from the self-consistency conditions, it is observed that the lowest resonance of scatterer affect very much on the dispersion than higher resonances. The lowest resonance is mainly caused by the density mismatch between matrix and particles, while higher ones by stiffness mismatch. The lowest resonance frequency shifts to high frequency range along the increase of particle volume fraction. This effect can be accurately predicted by the proposed theory. The transition of effective properties of composites obtained from the self-consistent method can be explained by considering two possible microstructures. Several phenomena similar to those in periodic structures, e.g., cut-off frequency, acoustical and optical branches, appear in dispersion curves. Predicted results reveal the phenomena common to most composites and they can be interpreted in a consistent manner. Dynamic characteristics of composites vary very much according to the variation of constituents and of the frequency of interest.