A method and apparatus for temporarily immobilizing a local area of tissue. In particular, the present invention provides a method and apparatus for temporarily immobilizing a local area of heart tissue to thereby permit surgery on a coronary vessel in that area without significant deterioration of the pumping function of the beating heart. The local area of heart tissue is immobilized to a degree sufficient to permit minimally invasive or micro-surgery on that area of the heart. The present invention features a suction device to accomplish the immobilization. The suction device is coupled to a source of negative pressure. The suction device has a series of suction ports on one surface. Suction through the device causes suction to be maintained at the ports. The device further is shaped to conform to the surface of the heart. Thus, when the device is placed on the surface of the heart and suction is created, the suction through the ports engages the surface of the heart. The suction device is further fixed or immobilized to a stationary object, such as an operating table or a sternal or rib retractor. Thus, the local area of the heart near the suction device is temporarily fixed or immobilized relative to the stationary object while suction is maintained. In such a fashion, the coronary artery may be immobilized even though the heart itself is still beating so that a bypass graft may be performed. In addition the suction device may be used in either a conventional, open-chest environment or in a minimally-invasive environment, e.g. endoscopic.