A method for performing intrastromal ophthalmic laser surgery requires Laser Induced Optical Breakdown (LIOB) of stromal tissue without compromising Bowman's capsule (membrane). In detail, the method creates cuts in the stroma over all, or portions of, a plurality of concentric cylindrical surfaces (circular or oval). Importantly, these cuts are all centered on the visual axis of the patient's eye. In accordance with the present invention, cuts can be made either alone or in conjunction with the removal of predetermined volumes of stromal tissue. The actual location of cuts in the surgery will depend on whether the treatment is for presbyopia, myopia, hyperopia or astigmatism.