A heart assist device in which an inflatable balloon or chamber is held against an outside surface of a curved arterial vessel by a wrap (20) formed from a flexible sheet-like material. The wrap (20) having a first end portion (22), a second end portion (30) and an intermediate portion (26) connecting together the first and second end portions (22, 30). The intermediate portion (26) comprising at least three separate elongate sections (26a-c) arranged in side by side array each connected at each end to a respective one of the end portions (22, 30) of the wrap (20). The improvement in that the laterally outer ones (26a,b) of the elongate sections are longer than the central one (26c) of them. As a result, if the wrap (20) was laid on a planar surface, the central (26c) one of the elongate sections would lie substantially in that plane and the laterally outer ones (26a,b) of the elongate sections would, intermediate their ends, project above that plane.
