The falling-head cased borehole analysis of Philip for determining the field-saturated hydraulic conductivity (Kfs) and sorptive number (α*) in the vadose zone was extended and assessed. The extension allows several water discharge configurations (vertical, radial, combined vertical and radial), variable length (L) and radius (a) of outflow screen, variable reservoir radius, and use of Excel Solver to calculate Kfs and α* via numerical optimization. The assessment used simulated borehole drawdown curves from HYDRUS-2D to determine the accuracy with which the Philip and extended solutions determined Kfs and α*. Using the Philip “flow efficiency correction,” CP = π2/8, and “gravity factor,” GP = equivalent sphere radius r0 (maximum gravity effect), caused the Philip and extended solutions to overestimate Kfs or α* by amounts ranging from a few percent in strong-capillarity soils to several orders of magnitude in weak-capillarity soils. Replacing CP with CE = 1 (no flow efficiency correction) and GP with GE = 0 (negligible gravity effect) in the extended solution resulted in accurate Kfs determinations (≤20% error) regardless of discharge geometry, screen configuration, drawdown range, or soil capillarity. Consistently accurate determination of α* required use of the CE and GE coefficients, 1 ≤ L/a ≤ 4, and avoidance of small borehole drawdowns. Solver-based determination of Kfs and α* using several heads distributed along the drawdown curve was less sensitive to measurement error and lack of data-model fit than the two-head approaches of Philip and others. The extended analysis improves the accuracy and utility of the falling-head cased borehole permeameter.