This paper presents a new spherical-flow cubic-analysis procedure for estimating horizontal and vertical permeabilities solely from pressure-transient data acquired at an observation probe of a dual-packer-probe wireline formation tester (WFT). The procedure applies for all inclination angles of the wellbore in a single-layer, 3D anisotropic porous medium. It does not require one to know the formation thickness or to obtain radial flow. It is shown that the procedure provides unique estimates of horizontal and vertical permeabilities from observation-probe pressure data obtained along both vertical and horizontal wellbores. However, for slanted-well cases, the analysis procedure yields two possible solutions for the horizontal and vertical permeabilities. Therefore, one must use a priori information on permeabilities, from sources such as core data or pretests, to help identify the appropriate solution for the slanted-well cases. For the more general case of a 3D anisotropic medium, except for the vertical wellbores, an estimate of the anisotropy ratio and the azimuth angle of the well are also required as inputs for determining the values of horizontal and vertical permeability with our analysis procedure. We illustrate the applicability of the proposed analysis procedure by considering two synthetic and two field packer-probe data sets from vertical and slanted wellbores.