This thesis is divided into four chapters. The first chapter briefly reviews existing approaches used in studying effective properties of a composite, and sets the scene for the work to follow. Chapter 2 is devoted to the study of a single-sphere scattering. The analytical approximations for scattering coefficients of a solid elastic sphere in a visco-acoustic medium for arbitrary partial wave orders are derived for both incident compressional and shear wave modes in the long-compressional wavelength limit, while imposing no restriction on the shear wavelength. The analytical results, within the validity domain of the solutions, are found to agree with numerical results obtained from the matrix inversion of boundary equations. The work in chapter 3 is concerned with the determination of effective dynamic properties. Used is a core-shell effective medium model to obtain analytical expressions for the effective bulk modulus and mass density for a random dispersion of solid spheres in a viscous fluid by incorporating the viscous nature of the host fluid into the model through wave mode coupling. By employing the CPA, the effective bulk modulus is obtained from the monopole mode and the effective density from the dipole mode. The bulk modulus is found to be quasi-static, whereas the effective density, due to the inclusion of shear-mediated contribution, is found to be dynamic. Chapter 4 is devoted to the study of effective density with spheroids. Extended is a hydrodynamic model by Ament from spherical to spheroidal particles in order to bring out the particle shape dependency on the effective dynamic density. Analytical expressions for the effective density for both prolate and oblate spheroids are obtained and demonstrated to significantly differ from the spherical case.