Abstract We develop a general theory of anisotropic diffusion in a cylindricalized lattice cell. The P N equations are derived for the normal and tilted fluxes in the cell and are related to the effective axial and radial diffusion coefficients which are used in homogeneous diffusion theory calculations. The theory is applied to a two region, non-absorbing cell, and Ps corrections to the axial diffusion coefficient are obtained. We also treat the case of a void by a special method involving an exact solution of the transport equation in the void region. The theoretical results are compared with those of Carter and of Benoist and also with some recent experiments of Bull and Connolly.