A system and method for resecting and transplanting corneal tissue is disclosed. In a recipient cornea, a resection depth from the anterior surface of the recipient cornea is determined based upon a biomechanical model of the recipient cornea. A resection incision for resecting a posterior portion of the recipient cornea is made at the resection depth. Preferably, the incision is made using a surgical laser. Optionally, a contact lens may be placed against the anterior surface of the recipient cornea, wherein the shape of the anterior surface is conformed to the shape of the contact lens.