The influence of particle shape and orientation on the thermal conductivity of low volume, particulate composites was examined through two-dimensional numerical simulations using the finite element method, FEM. The simulations demonstrate that the conductivity of such composites is influenced by not only the relative volume and conductivity of the embedded particles, but also their general shape, elongation, and orientation relative to the direction of global heat flow. The functional form of the Halpin-Tsai equation was utilized to characterize the composite thermal conductivity through a derived expression of the geometric distribution factor, zeta. The proposed expression of zeta differs from commonly assumed values and is shown to be highly dependent on the shape of the embedded particles. This approach was further extended to examine and explicitly characterize the anisotropic behavior of composites containing multiple, randomly distributed particles of a uniform size and shape based on their relative orientation. This work demonstrates the viability of using numerical tools to examine composites with complex geometries.