A method for grasping and holding tissue employs an apparatus including flexible sheet having walls that define adjoining top and bottom chambers which move together as a unitary part during use. The top and bottom walls of the flexible sheet conform to tissue and have corresponding first and second sets of holes. The method supplies suction to the top chamber and the first set of holes via the first fluid path to engage and hold tissue adjacent the top wall by suction forces applied through the first set of holes, and also supplies suction to the bottom chamber and the second set of holes via the second fluid path to engage and hold tissue adjacent the bottom wall by suction forces applied through the second set of holes.
