This work focuses on the simulation of shear wave propagation in the cornea. The underlying application is the detection, through elastography techniques, of pathologies associated with changes in tissue mechanics. Reproducing transient elastography poses several mechanical and numerical challenges. Intraocular pressure induces a nonlinear, often ill-posed problem, while the nearly incompressible behavior of the cornea leads to numerical locking and stability issues for explicit schemes. Moreover, the model is three-dimensional and anisotropic, making computational efficiency critical. We present a mathematical model of the cornea together with an explicit, second-order, energy-preserving numerical scheme that overcomes the limitations induced by incompressibility. Numerical results illustrate the effects of prestress and anisotropy on wave propagation.