A capillary barrier arises in unsaturated conditions at the contact of a fine layer of soil overlying a coarse layer of soil. If such a contact is tilted, infiltrating moisture in the fine layer will be diverted and flow down the contact as capillary diversion. Capillary barriers can occur naturally in layered heterogeneous systems, or they can be engineered for the purpose of diverting infiltration, for example, away from hazardous wastes. Recent theoretical analyses of capillary diversion have revealed some simple relations for the behavior of an idealized capillary barrier. Meanwhile, laboratory experiments and field investigations have shown much more complicated behavior. We have attempted to bridge the gap between the simple theoretical results and the more complicated laboratory and field observations by means of numerical experiments. Numerical modeling of capillary barriers present significant challenges because of the potential for gravitational instability which can give rise to strong space discretization and grid orientation effects. We have examined the ability of different finite difference techniques, such as harmonic weighting, upstream weighting, and higher-order differencing, to represent flow exclusion and leakage effects at capillary barriers. The numerical experiments show that analytical results previously obtained are reasonable, but that leakage occurs upstream of the theoretical breakthrough point. Furthermore, in the breakthrough region and downstream from it, the behavior is considerably more complicated than assumed in the theoretical analysis. Numerical experiments, with careful consideration of space discretization and grid orientation effects, reveal that the initial breakthrough allows sufficient leakage at the contact to partially dry the upper layer, making the barrier active again downstream. Finite difference schemes specifically designed to handle transient multiphase flows can adequately reproduce the broad features of flow diversion and leakage at capillary barriers. ¿ American Geophysical Union 1993