A device serves for temporarily immobilizing a tissue in an area of a pulsating blood vessel during a cardiac and thoracic surgical intervention. A pod of the device can be placed onto a tissue beneath a pulsating blood vessel. The pod has a rigid holder supporting a flexible element. The flexible element has suction openings in an area of contact with said tissue. The pod has a connector piece for the connecting to an underpressure source. A flexibility of said flexible element is in that said flexible element adapts to a shape of said tissue in said area of contact when placed on said tissue.