The material properties of the cornea are important determinants of corneal shape and refractive power. Corneal ectatic diseases, such as keratoconus, are characterized by material property abnormalities, are associated with progressive thinning and distortion of the cornea, and represent a leading indication for corneal transplantation. We describe a corneal elastography technique based on optical coherence tomography (OCT) imaging, in which displacement of intracorneal optical features is tracked with a 2-D cross-correlation algorithm as a step toward nondestructive estimation of local and directional corneal material properties. Phantom experiments are performed to measure the effects of image noise and out-of-plane displacement on effectiveness of displacement tracking and demonstrated accuracy within the tolerance of a micromechanical translation stage. Tissue experiments demonstrate the ability to produce 2-D maps of heterogeneous intracorneal displacement with OCT. The ability of a nondestructive optical method to assess tissue under in situ mechanical conditions with physiologic-range stress levels provides a framework for in vivo quantification of 3-D corneal elastic and viscoelastic resistance, including analogs of shear deformation and Poisson's ratio that may be relevant in the early diagnosis of corneal ectatic disease.