The prediction of infiltration of water into field soils requires measurements of the field-saturated hydraulic conductivity (Kfs) and the matric flux potential corresponding to field saturation (ϕm). We develop analytical solutions for (1) early-time, one-dimensional infiltration into slowly permeable soils such as clay liners under the conditions of an initial constant head followed by a falling head phase and (2) steady state, three-dimensional infiltration into permeable soils under the condition of steady state flow at a constant head followed by falling head conditions. Kfs and ϕm govern the shape of both solutions. The parameters are simultaneously identifiable, unique, and stable within the early-time solution; however, there is a limited range in which the parameters of the steady state solution are unique. Laboratory and field experiments based on both solutions gave physically realistic best fit parameter values using the solutions in inversion procedures. Field measurements gave an excellent correlation between Kfs from steady state constant head and falling head techniques. The correlation between ϕm values was somewhat lower. ¿ American Geophysical Union 1995