Present study optimizes the coefficients of the Kostiakov-Lewis infiltration Eq. and estimates water infiltration in the soil with the help of simulation of the advancing phase using the numerical solution of the Saint-Venant equations. In order to validate the numerical model, two series of field data measured in two regions of Iran were used and the results of the simulation were compared with actual field results. Also, using the Richards' Eq., the HYDRUS-1D software, the Hydrus-2D software, and a combination of the Hydrodynamics model with each of the mentioned methods the infiltration simulation and prediction of coefficients of the Kostiakov-Lewis infiltration Eq. were provided. The criteria for the accuracy of the methods were considered the comparison between the infiltration volumes of the water (calculated from each method) and the actual infiltration volume of the water in Furrow irrigation. The results illustrated that the combination of the Hydrodynamics model with each of the HYDRUS-1D, HYDRUS-2D software and the numerical solution of the Richards' Eq. increased the accuracy of the estimation process of the coefficients of the Kostiakov-Lewis's infiltration equation and the infiltration volume. So, the best and worst methods for simulating water infiltration through the soil has been introduced based on the less error between numerical and observed values of the infiltration volume as the combined method of the Hydrodynamics- HYDRUS 2D with NRMSE = 17.62% and numerical solution of the Richard's Eq. with NRMSE = 36.02%, respectively. The results illustrated that the error of the Hydrodynamics- HYDRUS-2D compared with the numerical solution of the Richard's Eq. (t(10) = −3.018) was significantly less value.