The changes of biomechanical properties, especially the elasticity of the ocular tissues, are closely related to some ophthalmic diseases. Currently, the ophthalmic optical coherence elastography (OCE) systems are dedicated either to the anterior segment or to the retina. The elasticity measurements of the whole eye remain challenging. Here we demonstrated an acoustic radiation force optical coherence elastography (ARF-OCE) method to quantify the elasticity of the cornea and the retina. The experiment results show that the Young's moduli of the cornea and the retina were 16.66 ± 6.51 kPa and 207.96 ± 4.75 kPa, respectively. Our method can measure the elasticity of the anterior segment and the posterior segment, and provides a powerful tool to enhance ophthalmology research.