A system for manipulating a heart during cardiac surgery permits coronary surgery on a beating heart while maintaining cardiac output unabated and uninterrupted. Circumflex coronary artery surgery can be performed using the system. The system locates a suspension head near the apical region of the heart and a gross support near the base of the heart near the AV groove. A frame is positioned within the patient's thoracic region and moves with the patient, and a surgical target immobilizer can be used to assist in the movement of the heart if desired. A special suction cup is used which accommodates multiplanar movement of the heart and the myocardium while also preventing heart tissue from interrupting the suction being applied to the heart. One form of the system can be used in minimally invasive surgery.