An assembly for implanting a prosthetic aortic valve in a native aortic valve of a patient's body, the assembly comprising: a delivery catheter comprising an inflatable balloon; and a prosthetic aortic valve configured to be radially collapsible to a collapsed state for introduction into the body on the delivery catheter and radially expandable using the balloon of the delivery catheter to an expanded state for implanting the prosthetic aortic valve at the native aortic valve in the body, the prosthetic aortic valve comprising: a radially collapsible and expandable annular frame, the frame having three angularly spaced commissure attachment posts and a plurality of angularly spaced, axial struts that are interconnected by at least three rows of circumferential struts including a first row of circumferential struts defining an inflow end of the frame, a second row of circumferential struts defining an outflow end of the frame, and a third row of circumferential struts positioned axially between the first and second rows of angled struts along the length of the frame and adjacent the second row of circumferential struts, each row of circumferential struts including struts arranged in a zig-zag pattern extending around the circumference of the frame; an annular skirt member positioned inside of and secured to the frame; and a leaflet structure comprising three leaflets, the leaflet structure having a scalloped lower edge portion secured to an inner surface of the skirt member and three commissures formed at adjacent sides of the leaflets, each commissure being attached to one of the commissure attachment posts, the skirt member disposed between the frame and the leaflet structure, characterized in that the the prosthetic aortic valve further comprises a reinforcing strip, separate from the skirt member, secured to an inner surface of the scalloped lower edge portion of the leaflet structure, wherein an upper edge of the skirt member has a zig-zag shape that generally follows the zig-zag pattern of and is attached with sutures to the third row of struts. a delivery catheter comprising an inflatable balloon; and a prosthetic aortic valve configured to be radially collapsible to a collapsed state for introduction into the body on the delivery catheter and radially expandable using the balloon of the delivery catheter to an expanded state for implanting the prosthetic aortic valve at the native aortic valve in the body, the prosthetic aortic valve comprising: a radially collapsible and expandable annular frame, the frame having three angularly spaced commissure attachment posts and a plurality of angularly spaced, axial struts that are interconnected by at least three rows of circumferential struts including a first row of circumferential struts defining an inflow end of the frame, a second row of circumferential struts defining an outflow end of the frame, and a third row of circumferential struts positioned axially between the first and second rows of angled struts along the length of the frame and adjacent the second row of circumferential struts, each row of circumferential struts including struts arranged in a zig-zag pattern extending around the circumference of the frame; an annular skirt member positioned inside of and secured to the frame; and a leaflet structure comprising three leaflets, the leaflet structure having a scalloped lower edge portion secured to an inner surface of the skirt member and three commissures formed at adjacent sides of the leaflets, each commissure being attached to one of the commissure attachment posts, the skirt member disposed between the frame and the leaflet structure, characterized in that the the prosthetic aortic valve further comprises a reinforcing strip, separate from the skirt member, secured to an inner surface of the scalloped lower edge portion of the leaflet structure, wherein an upper edge of the skirt member has a zig-zag shape that generally follows the zig-zag pattern of and is attached with sutures to the third row of struts. a radially collapsible and expandable annular frame, the frame having three angularly spaced commissure attachment posts and a plurality of angularly spaced, axial struts that are interconnected by at least three rows of circumferential struts including a first row of circumferential struts defining an inflow end of the frame, a second row of circumferential struts defining an outflow end of the frame, and a third row of circumferential struts positioned axially between the first and second rows of angled struts along the length of the frame and adjacent the second row of circumferential struts, each row of circumferential struts including struts arranged in a zig-zag pattern extending around the circumference of the frame; an annular skirt member positioned inside of and secured to the frame; and a leaflet structure comprising three leaflets, the leaflet structure having a scalloped lower edge portion secured to an inner surface of the skirt member and three commissures formed at adjacent sides of the leaflets, each commissure being attached to one of the commissure attachment posts, the skirt member disposed between the frame and the leaflet structure, characterized in that the the prosthetic aortic valve further comprises a reinforcing strip, separate from the skirt member, secured to an inner surface of the scalloped lower edge portion of the leaflet structure, wherein an upper edge of the skirt member has a zig-zag shape that generally follows the zig-zag pattern of and is attached with sutures to the third row of struts.