Basic closed-form theoretical results are derived relating the stress-strain sigma = sigma(epsilon), pressure-volume p = p(V), and ocular rigidity-pressure K = K(p) functions for a spherically symmetric eye of contant thickness and material properties. The results can be used to predict the pressure-volume and ocular rigidity behavior of both hyperopic and myopic eyes, in addition to the emmetropic case. The theoretical results are compared with eight different experimental studies from the literature. Five experimentally obtained mechanical variables, the pre-exponential stress-strain constant A (Pascals), the dimensionless exponential stiffening constant alpha, the pressure-volume globe stiffness intercept a (mm Hg/mm3), the globe stiffness slope b (mm-3), and the ocular rigidity K(mm-3) are found on average to agree with the theoretical predictions within a factor of 3 or better. Possible clinical applications might include measuring the ocular rigidity function K = K(p, Vo) to infer the mechanical strength of the corneo-scleral shell. The results may also be useful to help understand glaucoma dynamics as a function of refraction, and also with respect to tonometer calibration.