Abstract: Deformity, displacement and expulsion of the ocular tissues during eye surgery of the type in which there is a cut through the ocular wall, is opposed by the method and apparatus of this invention. According to the invention, the external surface of the eye is divided into two areas by defining a line on the external eye wall that forms a closed loop surrounding the sites where incisions through the eye wall are to be made or where cuts through the eye wall have already been made by traumatic injury. Then, according to the invention, air pressure higher than atmospheric is generated, when needed, in a work space outside the eye adjacent to that part of the external eye wall that lies within the closed loop, without compressing the external surfaces of the eye that lie outside the closed loop. The eye is concurrently stabilized against the applied pressure by attachment to a fixation device, usually at points along the line between the pressurized and non-pressurized zones of the external eye wall.