The irrigation advance problem in irrigation hydraulics has been spread across the engineering and soil science literature over a number of decades. The Lewis-Milne framework has been used extensively, but one problem has been to find a suitable infiltration equation. The infiltration advance solutions of Philip and Farrell, and Collis-George and Freebairn are compared to a new solution based on the linear soil infiltration equation. It is shown that the linear soil solution is able to give similar results to the Philip and Farrell solution at early stages of infiltration when this is valid, and the Collis-George and Freebairn solution at longer times when this is valid. The linear soil infiltration advance solution presented here is the first using physically meaningful parameters which is able to give adequate infiltration and advance behaviour over all time scales. To further test the linear soil concept, we inversely fit irrigation advance data to get the sorptivity, saturated hydraulic conductivity and infiltration rate behaviour of the soil using all three infiltration equations. The linear soil is shown to give the best fit for the infiltration behaviour to the measured results with an average r 2 of 0.98 compared to 0.84 for Philip and Farrell and 0.77 for Collis-George and Freebairn. The linear soil model was also the best fit using other statistical tests such as RMSE and RSR.