The magnetic field of the Jovian current disc has been modeled by using Euler functions and the Biot-Savart law applied to a series of concentric, but not necessarily coplanar, current rings. We find that a best fit to the Pioneer 10 outbound perturbation magnetic field data (Btotal-Bdipole) is obtained if the current disc is twisted (outer edges increasingly lag behind inner edges with radial distance) and also bent so as to tend toward parallelism with the Jovigraphic equator. The inner and outer radii of the disc appear to be about 7 RJ and 150 RJ, respectively, although some indication of a changing magnetopause location is apparent in the data. Because of the observed current disc penetrations, the bent disc also requires a deformation in the form of a bump or wrinkle whose axis tends also to exhibit spiraling. The radial dependence of the azimuthal current in the disc is not described by a simple power law, the outer region showing a smaller power law dependence. Modeling of the azimuthal field shows it to be due to a thin radial current sheet, but there is some evidence that this may, in fact, be due in large part to penetration of a tail current sheet as suggested by the Voyager observations.