In an earlier paper (Bland, Taylor, & Atherton), we presented detailed imaging Fabry-Perot observations of the ionized gas within Centaurus A over a wide field of view (7' x 5'). The TAURUS system was used to obtain 17,500 independent spectra of the H-alpha and [N II] lambda-6548 lines at both high spectral (almost-equal-to 36 km s-1 FWHM) and spatial (almost-equal-to 1".5 FWHM) resolution. We now present a class of geometric models that is successful in reproducing not only the general appearance of the dust lane system seen in broad-band optical images of the galaxy, but also the salient kinematic and morphological features observed in the Fabry-Perot observations. The resultant models are characterized by a thin warped disk geometry whose spatially averaged optical depth is sufficiently low as to allow emission from all positions within the disk to be observed. A key feature of these models is a structural discontinuity at intermediate radii, within which the structure twists away from the apparent plane defined by the dust band with decreasing radius. Such models offer a natural explanation for the absorption features identified in the spectra of SN 1986G and provide a geometric interpretation for the discrepancy between kinematic features identified in recent 21 cm observations and the dust band morphology. No evidence is found for significant noncircular or radial streaming motions. On the assumption of closed circular orbits, we demonstrated that the H-alpha velocity field can be interpreted in a manner consistent with the rotation curve expected from the spheroidal r1/4 law mass distribution indicated by photometric and velocity dispersion measurements of the stellar component. Hence we suggest that there is no evidence at present for a low M/L ratio in the nuclear regions of this system. While the geometry of the inner region of the prograde dust lane is inconsistent with a structure lying in the preferred plane of the host elliptical, a natural explanation for many features in the dust band geometry is provided by a partially self-gravitating, near-polar structure within an oblate-spheroidal or an oblate-triaxial system whose short axis lies near the plane of the sky.