Salvucci and Enthekabi (1995) proposed an approximate, time-implicit integral solution to the infiltration case for ponded soils bounded by a water table (i.e. under a hydrostatic equilibrium bottom boundary condition). In this work, we further developed this solution to make it numerically explicit in time and to account for unsteady rainfall conditions.. The new infiltration component was validated against a numerical solution of Richards'equation. In general, the presence of a shallow water table was found to be more important for fine soils than coarse soils. Soils that exhibit a marked air entry (bubbling pressure) on their soil water characteristic curve introduce also a distinct behavior for very shallow water table depths.