Purpose: To compare noncontact acoustic microtapping (AµT) OCT elastography (OCE) with destructive mechanical tests to confirm corneal elastic anisotropy. Design: Ex vivo laboratory study with noncontact AµT-OCE followed by mechanical rheometry and extensometry. Participants: Inflated cornea of whole-globe porcine eyes (n = 9). Methods: A noncontact AµT transducer was used to launch propagating mechanical waves in the cornea that were imaged with phase-sensitive OCT at physiologically relevant controlled pressures. Reconstruction of both Young's modulus (E) and out-of-plane shear modulus (G) in the cornea from experimental data was performed using a nearly incompressible transversely isotropic (NITI) medium material model assuming spatial isotropy of corneal tensile properties. Corneal samples were excised and parallel plate rheometry was performed to measure shear modulus, G. Corneal samples were then subjected to strip extensometry to measure the Young's modulus, E. Main Outcome Measures: Strong corneal anisotropy was confirmed with both AµT-OCE and mechanical tests, with the Young's (E) and shear (G) moduli differing by more than an order of magnitude. These results show that AµT-OCE can quantify both moduli simultaneously with a noncontact, noninvasive, clinically translatable technique. Results: Mean of the OCE measured moduli were E = 12 ± 5 MPa and G = 31 ± 11 kPa at 5 mmHg and E = 20 ± 9 MPa and G = 61 ± 29 kPa at 20 mmHg. Tensile testing yielded a mean Young's modulus of 1 MPa - 20 MPa over a strain range of 1% to 7%. Shear storage and loss modulus (G'/G'') measured with rheometry was approximately 82/13 ± 12/4 kPa at 0.2 Hz and 133/29 ± 16/3 kPa at 16 Hz (0.1% strain). Conclusions: The cornea is confirmed to be a strongly anisotropic elastic material that cannot be characterized with a single elastic modulus. The NITI model is the simplest one that accounts for the cornea's incompressibility and in-plane distribution of lamellae. AµT-OCE has been shown to be the only reported noncontact, noninvasive method to measure both elastic moduli. Submillimeter spatial resolution and near real-time operation can be achieved. Quantifying corneal elasticity in vivo will enable significant innovation in ophthalmology, helping to develop personalized biomechanical models of the eye that can predict response to ophthalmic interventions.