Based on the multiple scattering technique [K. F. Freed and M. Muthukumar, J. Chem. Phys. 69, 2657 (1978); 68, 2088 (1978); M. Muthukumar and K. H. Freed, J. Chem. Phys. 70, 5875 (1979)] previously applied to the study of suspensions of spheres and polymers, we propose an approach to the computation of the effective elastic properties of a composite material containing rigid, mono-sized, randomly dispersed, spherical particles. Our method incorporates the many-body, long-range elastic interactions among inclusions. The effective medium equations are constructed and numerically solved self-consistently. We have calculated the effective shear mu＇ and Young E＇ moduli, as well as the effective Poisson ratio sigma＇, as functions of the particle volume fraction Phi and of the Poisson ratio a of the continuous phase. Comparisons with two sets of experimental data-glass beads in a polymer matrix and tungsten carbide particles in a cobalt matrix (Wc/Co)-and to a previous theoretical solution, are also presented. Our model can predict the effective Poisson ratio of the Wc/Co system for Phi less than or equal to 1 and for the glass/polymer system for Phi less than or equal to 0.5. In particular, the present work describes accurately composites with a high volume fraction of inclusions, where a percolation transition occurs. Very good agreement with the experimental data are obtained for E＇ and mu＇ when Phi less than or equal to 0.4, for both systems.