A device for assisting and/or taking over the pumping function of the heart, with a multilayer sheathing part configured for compressing the heart at least in certain sections, wherein the sheathing part has at least one stabilization layer for shaping the sheathing part and at least one inner extensible augmentation layer, and wherein at least one cavity is formed between the stabilization layer and the augmentation layer, the cavity being inflatable and deflatable by a fluid, for cyclic compression of the heart. Provision is made for the stabilization layer to be inflatable with a fluid, at least in certain sections, in order to convert the sheathing part from a coiled and/or collapsed insertion state of the device in the body into an arched functional state, wherein the heart, in the functional state of the sheathing part, is at least partially sheathed and/or encompassed.