In the past forty years, much work has been done in the area of multiple scattering effects on the propagation of electromagnetic waves in a random particulate medium. This work is important to wave propagation in the atmosphere, the planetary sphere, and the ocean. Current research is aimed at high frequencies (gigahertz to terahertz). At these frequencies, multiple scattering effects become very important since the wavelength reduces to the size of a particle. The purpose of this thesis is to augment the Twersky theory of multiple scattering in a random particulate medium. Most applications of Twersky’s work use a far-field approximation and a point-particle assumption. At high frequencies, particle sizes may be large relative to a wavelength; therefore, the point-particle assumption is inaccurate. Under a low-density approximation, this thesis introduces a scattering operator, which defines closed equations for the fields due to multiple scattering. The low-density approximation holds for many media (e.g. clouds and rain). The scattering operator may be solved for various particle shapes, eliminating the need for the point-particle assumption. / Master of Science