The irrigation advance problem has been around for a number of decades in irrigation hydraulics and has spread across the engineering and soil science literature.  The Lewis-Milne volume balance framework and its solution by Philip and Farrell using Laplace transforms have been extensively used, but finding a suitable infiltration equation has been a problem.  The Philip two-term infiltration equation is only suitable for early time irrigation and will underestimate the infiltration and over estimate the advance at longer time.  At long times the approach of Collis-George can be used but this is unsuitable at short times, where it over estimates the infiltration and underestimates the advance.  The linear soil infiltration function is shown to give suitable infiltration behaviour and a solution is described which has the correct behaviour over all time scales. We consider the forward problem and compare the predictions using the Philip two-term, Collis-George and linear soil infiltration functions for a range of soil properties.  We also investigate the inverse problem of deriving the soil hydraulic properties from advance data in border-dyke irrigation. Our method can also be used to model the simultaneous infiltration and radial spread of water on the soil surface from a point source of supply.