The Variable-Head Borehole Permeameter (VHBP) method is a long-standing international standard for in-situ measurement of field-saturated hydraulic conductivity, K_FS, in natural and engineered porous media.  Its applicability is restricted, however, because traditional VHBP theory does not apply for unsaturated or deformable porous media, and because precise knowledge of the appropriate porous medium boundary condition at the borehole outlet/inlet zone (screen) is required for accurate K_FS determination.  This study extends the traditional VHBP theory to include saturated, unsaturated, rigid and deformable porous media, and also clarifies the boundary condition at the screen.  Using a recent VHBP analysis developed for rigid, unsaturated porous media, it is shown that change in porous medium water content, Δθ, can be extended to include change in porosity (deformation) as well as change in degree of saturation.  It is also shown that the appropriate boundary condition at the borehole screen is antecedent pore water pressure head, H_a, for saturated porous media, but effective wetting front pressure head, ψ_f (or sorptive number, α*), for unsaturated porous media.  The K_FS, Δθ, H_a, and ψ_f (or α*) parameters can be determined using numerical optimization (e.g. “Solver” in the Excel spreadsheet) to curve-fit the extended VHBP analysis directly to borehole head versus time measurements; however, fitting to the velocity graph (borehole head plotted against change in head with time) is generally less problematic.  In a cursory assessment of the extended VHBP analysis, K_FS was determined with ≤ 7 % error, Δθ with ≤ 15 % error, H_a with ≤ 1.4 % error, and ψ_f with ≤ 0.5 % error, which is more than sufficient accuracy for most applications.