Most measurements of the steady state unsaturated hydraulic conductivity require the measurement of the pressure and the flow rate in a laboratory column under normal drainage conditions. However, centrifugal techniques allow the creation of experimental conditions that are more suitable for fast and accurate measurements of the hydraulic conductivity function. Explicit algebraic equations for the parameters were developed for various forms of the hydraulic conductivity function, including the log linear form, the power form, and the more general inverse-power form. Parameter estimation of the unsaturated hydraulic conductivity function is accomplished through the use of exact and approximate solutions derived from the governing one-dimensional unsaturated flow equation for a soil medium experiencing a centrifugal force. The exact solution pertains to the log linear hydraulic conductivity function. The approximate solutions were obtained through perturbation expansion for the other forms of the hydraulic conductivity. The approximate solutions showed good agreement with the numerical solution for two soil types and various experimental conditions. The parameter estimation procedure was tested using a hypothetical pressure distribution and was found to give fairly accurate reproduction of the assumed unsaturated hydraulic conductivity. ¿ 1999 American Geophysical Union