This invention provides an organ positioning device and method that employs suction to hold organ tissue to the device. The device allows the organ, for example, heart to be positioned in a desired orientation but otherwise allowing movement of the heart as the heart beats. The device is designed to be relatively atraumatic to heart tissue. Generally, the device comprises a resiliently flexible suction head having a plurality of legs that flex to conform to the surface of the heart. The suction head has vacuum passageways in fluid communication with the legs to apply suction between the legs and the surface of the heart.