A wrap (20) for securing about a blood vessel (36) by encasing a section of the vessel. The wrap (20) being of thin flexible construction having two ends (22, 24) and two sides (26, 28). The wrap (20) is more elastic or stretchable at, near, or along at least some of its sides (22, 24) compared to at, near, or along its center, to provide strain relief from wrapped to unwrapped aorta. The wrap (20) is not inelastic, so that loss of aortic compliance is minimized or enhanced. The wrap (20) is adapted to apply, in use, less compressive force at, near, or along at least some of its sides (22, 24) compared to at, near, or along its center.