New formulae giving the position of the wetting front and the surface water content during horizontal infiltration when the surface flux is specified are presented. The flux can be any smoothly-varying function of time, though only nonhysteretic flow is modeled. The approximation is in excellent agreement with an exact analytical solution existing for constant boundary flux and a nonlinear Fujita diffusivity. It is also successfully compared with a further exact solution existing for a particular time-varying flux.