A new algorithm for the simulation of one-dimensional liquid infiltration into variably saturated porous media is presented. The present model, which is based on Richards' equation, tracks the infiltrating front position by adding, at each time step, one spatial grid point to the edge of the infiltrating liquid. Fluxes are computed using the Kirchhoff transform, which allows one to handle the step change of the pressure head encountered at the front location. The algorithm performance was tested for three published cases: (1) an analytical solution of the water infiltration problem valid for homogeneous dry soils, (2) experimental nonaqueous phase liquid infiltration data obtained in a laboratory column, and (3) water infiltration into a dry, layered soil system. The results of the test cases demonstrate the computational efficiency of the algorithm and its ability to handle steep pressure gradients and front discontinuities with relatively coarse grids and without sacrificing numerical accuracy. ¿ 1999 American Geophysical Union