The anisotropic mechanical properties of bovine eye lenses were measured using cavitation rheology over a range of length scales. The technique involves inducing a cavity at the tip of a syringe needle in different regions of the lens. Effective Young's moduli of the nucleus and cortex of the lens were determined, as approximately 11.8 and 0.8 kPa, respectively, on macroscopic length scales. We also measured the mechanical properties of the lens on the length scale of a single cell, suggesting that the stiffness significantly decreased from that in the bulk measurements for both the nucleus and cortex. In addition, during the growth of the cavity anisotropic propagation in the cortex was observed, while in the nucleus, the propagation was isotropic. We further explored the elasticity of the cavity deformation, showing both elastic and inelastic deformation occurred in the nucleus with equal contributions while deformation in the cortex was elastic and reversible.