A device for assisting the operation of a natural heart is provided. A supporting jacket shaped to surround at least a portion of a heart has an expandable membrane attached to the inside wall of the jacket so that the membrane faces the heart. An inflatable cavity is formed between the jacket and the membrane. The cavity is connected to an expandable fluid reservoir via a length of flexible tubing. Pumps are used to pump fluid back and forth between the cavity and the reservoir. The cavity if inflated as the heart contract to aid the heart in pumping blood. The cavity is deflated as the heart relaxes to allow the heart to refill with blood. The cycle of pumping fluid is synchronized with the cardiac cycle.