A prosthetic heart valve implantation system, comprising: a balloon-expandable prosthetic heart valve having a compressed state for delivery, an operating shape when in an expanded state, and a construction that has a non-uniform expansion resistance profile along its axial length; wherein the prosthetic heart valve has an inflow end, an outflow end and an outer frame or stent supporting three separate flexible leaflets within, the leaflets extending into a cylindrical space defined within the outer frame or stent, the prosthetic heart valve being stiffer near the inflow end than near its outflow end; wherein each of the three separate leaflets is secured to the outer frame or stent and to the respective other two leaflets along lines of commissures, and a flexible material forming the leaflets is attached to the outer stent via a fabric intermediary and a plurality of sutures; and wherein the outer frame or stent is formed by a plurality of axially-oriented and circumferentially angled struts, and generally defines a tube in the operating shape of the prosthetic heart valve; and an expansion member (40; 50; 60; 70; 90; 100) disposed within the prosthetic heart valve in its compressed state characterised in that the expansion member accommodates the non-uniform expansion resistance in the prosthetic heart valve and is configured to apply non-uniform radially outward forces to the prosthetic heart valve along its axial length to convert it into its desired tubular shape in the expanded state; wherein the prosthetic heart valve is axially positioned on the expansion member (40; 50; 60; 70; 90; 100) such that portions of the expansion member (40; 50; 60; 70; 90; 100) that are capable of applying the largest initial radially outward forces are in registry with stiffer areas of the prosthetic heart valve. a balloon-expandable prosthetic heart valve having a compressed state for delivery, an operating shape when in an expanded state, and a construction that has a non-uniform expansion resistance profile along its axial length; wherein the prosthetic heart valve has an inflow end, an outflow end and an outer frame or stent supporting three separate flexible leaflets within, the leaflets extending into a cylindrical space defined within the outer frame or stent, the prosthetic heart valve being stiffer near the inflow end than near its outflow end; wherein each of the three separate leaflets is secured to the outer frame or stent and to the respective other two leaflets along lines of commissures, and a flexible material forming the leaflets is attached to the outer stent via a fabric intermediary and a plurality of sutures; and wherein the outer frame or stent is formed by a plurality of axially-oriented and circumferentially angled struts, and generally defines a tube in the operating shape of the prosthetic heart valve; wherein the prosthetic heart valve has an inflow end, an outflow end and an outer frame or stent supporting three separate flexible leaflets within, the leaflets extending into a cylindrical space defined within the outer frame or stent, the prosthetic heart valve being stiffer near the inflow end than near its outflow end; wherein each of the three separate leaflets is secured to the outer frame or stent and to the respective other two leaflets along lines of commissures, and a flexible material forming the leaflets is attached to the outer stent via a fabric intermediary and a plurality of sutures; and wherein the outer frame or stent is formed by a plurality of axially-oriented and circumferentially angled struts, and generally defines a tube in the operating shape of the prosthetic heart valve; and an expansion member (40; 50; 60; 70; 90; 100) disposed within the prosthetic heart valve in its compressed state characterised in that the expansion member accommodates the non-uniform expansion resistance in the prosthetic heart valve and is configured to apply non-uniform radially outward forces to the prosthetic heart valve along its axial length to convert it into its desired tubular shape in the expanded state; wherein the prosthetic heart valve is axially positioned on the expansion member (40; 50; 60; 70; 90; 100) such that portions of the expansion member (40; 50; 60; 70; 90; 100) that are capable of applying the largest initial radially outward forces are in registry with stiffer areas of the prosthetic heart valve.