Numerically simple models for soil transport processes based on the use of the slopes of soil parameter curves as dynamic parameters have proved to be a stable and accurate supplement to other models. In this study, the recently presented moving mean slope (MMS) model for vertical, unsaturated water flow is evaluated, using series and numerical analyses. Results show that the MMS model takes into account additional parameters in the estimation of the soil hydraulic conductivity (K) between the calculation depths compared with the arithmetic or geometric mean value considerations used normally. This suggests that the MMS modeling approach implicitly provides a good estimation of the nonlinear change ofKwith soil depth and explains the observation that it is often possible to use larger depth and time increments in the MMS model than in many of the traditionally used numerical models. The vertical MMS model is modified for horizontal flow, and the corresponding criterion for avoiding numerical errors in the calculations is derived. The agreement between horizontal flow calculations using the simple MMS model and the Crank-Nicolson finite difference model is excellent. A new series expression for the horizontal flow velocity is obtained by using a reformulated, integrated version of the horizontal Darcy flow equation. After a short infiltration time, only the first few terms of the series expression are quantitatively important. This seems convenient for analyzing and mathematically describing infiltration into soils.