A mathematical analysis of ocular pneumoplethysmography is presented, based on the physiological, anatomical, and biomechanical properties of the eye. Ocular pneumoplethysmography is a clinical procedure involving elevation of intraocular pressure, by application of a suction cup to the sclera, to a level that exceeds ophthalmic artery systolic pressure. As decay in intraocular pressure is allowed, return of retinal artery pulsations indicates ophthalmic artery systolic pressure. We obtain a quantitative relationship between increase in intraocular pressure and applied vacuum, and compare the theoretical predictions with experiments on rabbits in which a variable descending vacuum was applied to bilateral scleral eyecups. The bilateral intraocular pressures were simultaneously recorded from cannulae in the respective vitreous bodies, and the pressures at which return of ocular pulsations were observed were correlated with the scleral vacuums. Regression lines were calculated for three serial determinations in each animal, with two groups of animals distinguished by the inner diameter of the eyecups used. The theoretical results indicate that the relationship between intraocular pressure increase and applied vacuum is independent of Young's modulus, and depends primarily on the ratio of the diameter of the vacuum cup to the diameter of the eye.