New, constant-head permeameter analyses for steady flow in cased boreholes were developed for in situ measurement of field-saturated hydraulic conductivity (Kfs) and matric flux potential (ϕm) in the vadose zone. The Kfs and ϕm parameters can be determined using calculations based on multiple ponded heads, dual heads, or a single head. The accuracy of the analyses was assessed using HYDRUS-2D simulations of steady borehole discharge (Qt) vs. ponded head (H) for specified Kfs, ϕm, soil capillarity (α* = Kfs/ϕm), and length (L) and radius (a) of the borehole screen. The multiple-head and dual-head calculations provided accurate Kfs determinations (≤26% error) for the full range of tested capillarity (0.1 ≤ α* ≤ 14.45 m−1), screen radius (a = 3–7.5 cm), screen length (L = 0–45 cm), and head (H = 3–200 cm). The multiple-head and dual-head calculations of ϕm were similarly accurate (≤25% error) for high-capillarity soils (α* ≤ 1 m−1), and for L/a ≤ 1 in moderate- to negligible-capillarity soils (α* ≥ 9 m−1). The ϕm calculations were not accurate, however, in moderate- to negligible-capillarity soils with L/a > 1. The single-head calculation with α* estimated using soil texture and structure categories was accurate only for Kfs determination (≤23% error) in soils with moderate to negligible capillarity. For ϕm determination, and for Kfs determination in high-capillarity soils, the single-head calculation requires accurately known α* values. The analyses appear promising for Kfs and ϕm determination in the vadose zone, and further development and testing are ongoing.