Abstract: A device is provided for locally immobilizing a beating heart, in order to avoid tears or hematomas of the heart tissue during the application of strong pressure or suction forces. The device is particularly useful during an anastomosis procedure between a bypass conduit and a coronary vessel of the anterior wall of the left ventricle. The device includes a fork-like platform with two essentially parallel fork blades that form an intermediate space therebetween. The intermediate space has a width which corresponds to one to five times the width of a coronary vessel that is to be arranged in the intermediate space. At least one opening is provided on each of the fork blades adjacent to the intermediate space. Elements that can be guided through the openings and secured to a fixing device are provided for winding around the coronary vessel.