Application of the air-puff swept source optical coherence tomography (SS-OCT) instrument to determine the influence of viscoelasticity on the relation between overall the air-puff force and corneal apex displacement of porcine corneas ex vivo is demonstrated. Simultaneous recording of time-evolution of the tissue displacement and air pulse stimulus allows obtaining valuable information related in part to the mechanical properties of the cornea. A novel approach based on quantitative analysis of the corneal hysteresis of OCT data is presented. The corneal response to the air pulse is assessed for different well-controlled intraocular pressure (IOP) levels and for the progression of cross-linking-induced stiffness of the cornea. Micrometer resolution, fast acquisition and noncontact character of the air-puff SS-OCT measurements have potential to improve the in vivo assessment of mechanical properties of the human corneas.