**ABSTRACT: **We describe an analysis of neutron transport in a modeled 2-D (transport in a plane) pebble-bed reactor (PBR) core consisting of fuel discs stochastically piled up in a square box. Specifically, we consider the question of whether the force of gravity, which plays a role in this piling, affects the neutron transport within the system. Monte Carlo codes were developed for (i) deriving realizations of the 2-D core, and (ii) performing 2-D neutron transport inside the heterogeneous core; results from these simulations are presented. In addition to numerical results, we present preliminary findings from a new theory that generalizes the atomic mix approximation for PBR problems. This theory utilizes a non-classical form of the Boltzmann equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We take the diffusion limit of this equation and derive an anisotropic diffusion equation. (The diffusion is anisotropic because the mean and mean square distances between collisions in the horizontal and vertical directions are slightly different.) We show that the results predicted using the new theory more closely agree with experiment than the atomic mix results. We conclude by discussing plans to extend the present work to 3-D problems, in which we expect the anisotropic diffusion to be more pronounced.