The field-saturated hydraulic conductivity Kfs can be obtained from measurements of the long-time steady flow rates from ring infiltrometers by assuming either that the soil is a ''Green and Ampt'' soil that has a relationship between hydraulic conductivity K and soil water pressure &psgr;, such that K=Kfs, 0≥&psgr;≥&psgr;f; K→0, &psgr;≤&psgr;f, or that the soil is a ''Gardner'' soil with an exponential relationship K=Kfs exp(&agr;&psgr;), where &agr; is a constant. It is shown that infiltration into a Green and Ampt soil from a surface source with zero head is the same as that for a Gardner soil with &agr;→∞ (gravity dominant) and with a surface source at a head ‖&psgr;fs‖. The shape factor G calculated for Gardner soils using a numerical solution of Richards's equation is used to calculate Kfs and &agr; from ring infiltrometer tests based on Q=<aH/G+a/(&agr;G)+&pgr;a2>Kfs, where Q is the steady state flow rate, H is the constant ponded head, and a is the ring radius. The equivalent G factor for Green and Ampt soils calculated using electric analogue solutions of Laplace's equation is shown to agree very well with the numerical solution. The slope of the linear relationship between the shape factor and the depth of insertion of the ring divided by the radius of the ring is shown to have a slope approximately equal to 1/&pgr;. ¿ American Geophysical Union 1993