This paper develops a new von Mises ellipse based on backup pressure (internal pressure for collapse and external pressure for burst), so the new API collapse equations with dependence on internal pressure can be shown simultaneously on the same plot with the ellipse. Unlike the current ellipse used for casing and tubing design which is approximate, the new ellipse is exact for collapse, burst, and axial loads. Without the new ellipse, the approximate ellipse will continue to be used, and the new API collapse equations must be plotted separately. Example cases demonstrate the advantages of the new ellipse, including increased accuracy. Results help clarify many questions about the new API collapse equations, namely where they come from and how to use them.