Apparatus for delivering a collapsible and re-expandable prosthetic heart valve to an implant site in a patient comprising: a valve support structure (140, 140', 120, 150, 150') around which the valve may be disposed in a collapsed condition; a sheath structure (110a-b) for surrounding the valve on the valve support structure, the sheath structure including a first sheath part that may cover a first axial end part of the valve in the collapsed condition, and a second sheath part that may cover a second axial end part of the valve in the collapsed condition; and a means for moving one of the sheath parts relative to the other sheath part to uncover the valve for expansion at the implant site, the valve having first and second surface portions (21a, 21b) that face in respective opposite first and second directions along an axis around which the valve may be disposed on the valve support structure (140; 120/140'/150'), and the valve support structure having third and fourth (141b, 151b) surface portions that respectively face in the second and first directions, the first and third surface portions being positionable adjacent to and facing one another in use, and the second and fourth surface portions being positionable adjacent to and facing one another in use to substantially prevent relative movement of the valve and the valve support structure along said axis while the valve is disposed around the valve support structure in the collapsed condition characterised in that the apparatus comprises a means for drawing (210a-c) a portion of the valve that has been uncovered by the sheath structure radially inwardly toward the valve support structure. a valve support structure (140, 140', 120, 150, 150') around which the valve may be disposed in a collapsed condition; a sheath structure (110a-b) for surrounding the valve on the valve support structure, the sheath structure including a first sheath part that may cover a first axial end part of the valve in the collapsed condition, and a second sheath part that may cover a second axial end part of the valve in the collapsed condition; and a means for moving one of the sheath parts relative to the other sheath part to uncover the valve for expansion at the implant site, the valve having first and second surface portions (21a, 21b) that face in respective opposite first and second directions along an axis around which the valve may be disposed on the valve support structure (140; 120/140'/150'), and the valve support structure having third and fourth (141b, 151b) surface portions that respectively face in the second and first directions, the first and third surface portions being positionable adjacent to and facing one another in use, and the second and fourth surface portions being positionable adjacent to and facing one another in use to substantially prevent relative movement of the valve and the valve support structure along said axis while the valve is disposed around the valve support structure in the collapsed condition characterised in that the apparatus comprises a means for drawing (210a-c) a portion of the valve that has been uncovered by the sheath structure radially inwardly toward the valve support structure.