An implantable prosthetic valve comprising: an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, the frame defining an axial direction extending from the inflow end to the outflow end ; a leaflet structure positioned within the frame and secured thereto; and an annular outer skirt positioned around an outer surface of the frame , wherein the outer skirt comprises: an inflow edge secured to the frame at a first location, an outflow edge secured to the frame at a second location; and an intermediate portion between the inflow edge and the outflow edge that comprises slack that buckles radially outwards from the inflow and outflow edges of the annular outer skirt when the valve is in the expanded configuration; characterized in that the outer skirt further comprises: (a) a fabric that is stiffer in the axial direction of the valve compared to a circumferential direction to enhance the radial outward buckling of the slack; and/or (b) a self-expandable fabric comprising fibers made of shape memory material having a shape memory set to enhance the radially outward buckling of the slack of the outer skirt . an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, the frame defining an axial direction extending from the inflow end to the outflow end ; a leaflet structure positioned within the frame and secured thereto; and an annular outer skirt positioned around an outer surface of the frame , wherein the outer skirt comprises: an inflow edge secured to the frame at a first location, an outflow edge secured to the frame at a second location; and an intermediate portion between the inflow edge and the outflow edge that comprises slack that buckles radially outwards from the inflow and outflow edges of the annular outer skirt when the valve is in the expanded configuration; characterized in that the outer skirt further comprises: (a) a fabric that is stiffer in the axial direction of the valve compared to a circumferential direction to enhance the radial outward buckling of the slack; and/or (b) a self-expandable fabric comprising fibers made of shape memory material having a shape memory set to enhance the radially outward buckling of the slack of the outer skirt . an inflow edge secured to the frame at a first location, an outflow edge secured to the frame at a second location; and an intermediate portion between the inflow edge and the outflow edge that comprises slack that buckles radially outwards from the inflow and outflow edges of the annular outer skirt when the valve is in the expanded configuration; characterized in that the outer skirt further comprises: (a) a fabric that is stiffer in the axial direction of the valve compared to a circumferential direction to enhance the radial outward buckling of the slack; and/or (b) a self-expandable fabric comprising fibers made of shape memory material having a shape memory set to enhance the radially outward buckling of the slack of the outer skirt . (a) a fabric that is stiffer in the axial direction of the valve compared to a circumferential direction to enhance the radial outward buckling of the slack; and/or (b) a self-expandable fabric comprising fibers made of shape memory material having a shape memory set to enhance the radially outward buckling of the slack of the outer skirt . <EOS>