A vertical long soil column subject to rainfall filtrating through the upper end of the column has been considered. The mathematical formulation of this physical model, based on the theory of fluid flows in a nonsaturated porous medium, leads to a one-phase, nonlinear parabolic free boundary problem, the free boundary being the wetting front. For such a problem, theorems on existence, uniqueness, and continuous dependence on the data and the coefficients appearing in its mathematical equations have been proved.