Recent observations of galaxy luminosity profiles and dark matter simulations find luminosity and mass distributions characterized by central cusps rather than finite core radii. We introduce and implement a set of cusped ellipsoidal lens models which include limits similar to the Jaffe, Hernquist, eta and NFW models and apply them to the gravitational lenses APM 08279+5255 and B 1933+503. A successful model of APM 08279+5255 with its central, odd image requires a very shallow cusp, $gamma ltorder 0.4$ where $rho propto r^{-gamma}$ as $rto 0$, which is similar to a core rather than the favored $1 ltorder gamma ltorder 2$ cusps. B~1933+503, by contrast, is well modeled with a steep density cusp, $1.6 ltorder gamma ltorder 2.0$.
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