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 that include limits similar to the Jaffe, Hernquist, η and NFW models and apply them to the gravitational lenses APM 08279+5255 and B1933+503. A successful model of APM 08279+5255 with its central, odd image requires a very shallow cusp, γ<~0.4, where ρ~r-γ as r-->0, which is similar to a core rather than the favored 1<~γ<~2 cusps. B1933+503, by contrast, is well modeled with a steep density cusp, 1.6<~γ<~2.0.