Empirical equations and physically based equations used to describe vertical infiltration into simple soil systems are compared with experimental data. An empirical equation is proposed which satisfies the conditions that cumulative infiltration is proportional to (time)½ at short times and reaches a steady state infiltration rate at long times. This equation, i = i0 (tanh T)½ + Kt, describes the observed behavior of simple soil systems at all times, where i is the cumulative infiltration at time t, K is the infiltration rate at steady state, i0 = S(tc)½, and T = t/tc. The sorptivity S (Philip, 1957) and a time parameter tc (Collis-George, 1974) are soil properties determinable experimentally. The Green and Ampt equation and the Horton equation do not satisfy observed behavior at all times, the former failing at long times and the latter at short times. The equation of van der Want (1976), the linearized Fokker-Planck equation of Philip (1969), and the nonlinearized Fokker-Planck equation of Knight and Philip (Philip, 1974) do not describe the observed behavior of simple soil systems over the whole time range as precisely as the proposed empirical equation. Since i0 is not an independent part of these equations, its numerical value is defined by the independent parameters S and K, and for the materials examined it is generally not the same as the experimental value. Procedures are outlined for treating experimental data, not necessarily complete for all times, to produce the three parameters, K, S, and tc for simple systems, and for describing infiltration into cracking clays or in cases where ultrashort time effects occur.