A prosthetic aortic heart valve including a stent that supports a leaflet assembly, wherein the valve is radially compressible to a compressed state for delivery through the body to a deployment site and expandable to its functional size at the deployment site, the stent being formed from a plurality of longitudinally extending, generally sinusoidal shaped struts, the struts being formed with alternating bends and being secured to each other at nodes formed from vertices of adjacent bends so as to form a mesh structure, the stent having an inflow end and an outflow end, the mesh structure having a curved shape along its entire length that gradually increases in diameter from an outflow end portion to an intermediate section, then gradually decreases in diameter from the intermediate section to a location on an inflow end portion, and then gradually increases in diameter to form a flared portion terminating at the inflow end, the leaflet assembly comprising three leaflets (34a; 34b; 34c) made of a flexible material, each leaflet (34a; 34b; 34c) having an inflow end portion and an outflow end portion, the leaflet assembly including an annular reinforcing skirt that is secured to outer surfaces of the inflow end portions of the leaflets (34a; 34b; 34c) at a suture line adjacent an inflow end of the valve, an inflow end portion of the leaflet assembly being secured to the stent by suturing the skirt to struts of a lower section of the stent; wherein the valve is configured to be implanted such that the lower section of the stent is positioned within an aortic annulus, the intermediate section extends above the aortic annulus into the Valsalva's sinuses, and the flared portion terminating at the inflow end extending below the aortic annulus; and wherein the intermediate section and the flared portion terminating at the inflow end are greater in diameter than the annulus so as to assist in retaining the prosthetic aortic heart valve in place in the native valve against forces tending to dislodge the prosthetic aortic heart valve in the upstream and downstream directions; wherein when the prosthetic aortic heart valve is in an expanded state, the intermediate section has a first diameter, the inflow end portion has a second, minimum diameter, the inflow end has a third diameter, and the outflow end portion has a fourth diameter, where the second diameter is less than first and third diameters (D1, D3), and. wherein the first and third diameters (D1, D3) are greater than the diameter of the native annulus in which the prosthetic aortic heart valve is to be implanted. the stent being formed from a plurality of longitudinally extending, generally sinusoidal shaped struts, the struts being formed with alternating bends and being secured to each other at nodes formed from vertices of adjacent bends so as to form a mesh structure, the stent having an inflow end and an outflow end, the mesh structure having a curved shape along its entire length that gradually increases in diameter from an outflow end portion to an intermediate section, then gradually decreases in diameter from the intermediate section to a location on an inflow end portion, and then gradually increases in diameter to form a flared portion terminating at the inflow end, the leaflet assembly comprising three leaflets (34a; 34b; 34c) made of a flexible material, each leaflet (34a; 34b; 34c) having an inflow end portion and an outflow end portion, the leaflet assembly including an annular reinforcing skirt that is secured to outer surfaces of the inflow end portions of the leaflets (34a; 34b; 34c) at a suture line adjacent an inflow end of the valve, an inflow end portion of the leaflet assembly being secured to the stent by suturing the skirt to struts of a lower section of the stent; wherein the valve is configured to be implanted such that the lower section of the stent is positioned within an aortic annulus, the intermediate section extends above the aortic annulus into the Valsalva's sinuses, and the flared portion terminating at the inflow end extending below the aortic annulus; and wherein the intermediate section and the flared portion terminating at the inflow end are greater in diameter than the annulus so as to assist in retaining the prosthetic aortic heart valve in place in the native valve against forces tending to dislodge the prosthetic aortic heart valve in the upstream and downstream directions; wherein when the prosthetic aortic heart valve is in an expanded state, the intermediate section has a first diameter, the inflow end portion has a second, minimum diameter, the inflow end has a third diameter, and the outflow end portion has a fourth diameter, where the second diameter is less than first and third diameters (D1, D3), and. wherein the first and third diameters (D1, D3) are greater than the diameter of the native annulus in which the prosthetic aortic heart valve is to be implanted.