A flux-corrected transport (FCT) based numerical algorithm is developed to model the solute transport equation in heterogeneous variably saturated soils. The fully Eulerian algorithm is designed to model very steep gradients without the characteristic numerical diffusion/dispersion found in standard finite difference schemes. This algorithm can handle both small and infinite grid Peclet numbers but is limited to grid Courant numbers less than or equal to 0.5. Since useful results can be obtained for infinite Peclet numbers, the algorithm can be used to trace water movement when coupled with a numerical model for Richards' equation. We used the FCT based algorithm in conjunction with Richards' equation to a model a hypothetical experiment at the Las Cruces Trench site. In this numerical experiment, water with tracer is applied across the top of a 24-m-wide domain. The two-dimensional distribution for the hydraulic properties estimated during site characterization is used to define the soil model. The predicted flow and tracer transport is quite complex. The movement of the wetting front appears to be heavily influenced by the old water, whereas the new water tends to bypass much of the old water indicating preferential flow. ¿ American Geophysical Union 1994