Embodiments of a radially collapsible and expandable prosthetic heart valve are disclosed. The prosthetic valve can comprise an annular frame, leaflets, an inner skirt, and an outer skirt. The outer skirt can be secured to the outside of the inflow end portion of the frame, the outer skirt having longitudinal slack that buckles outward radially when the valve is in the expanded configuration and which lies flat when the valve is in the collapsed configuration. In some embodiments, the outer skirt is stiffer in the axial direction of the valve than in the circumferential direction of the valve. In additional embodiments, the outer skirt comprises a self-expandable fabric comprising fibers made of a shape memory material having a shape memory set to enhance the radially outward buckling of the outer skirt. Methods of crimping such valves to a collapsed or partially collapsed configuration are also disclosed.