An assembly for transvascular replacement of a native aortic heart valve can have a radially collapsible and self-expandable prosthetic heart valve and a delivery apparatus. The valve can have an annular metal frame made of a shape-memory material with a plurality of posts extending from an end portion of the frame. The delivery apparatus can have a shaft comprising a valve connection portion that is releasably coupled to the posts of the valve. The valve connection portion can have a plurality of discrete radially facing recesses that receive the posts. The delivery apparatus can have a delivery sheath that is positioned around the prosthetic heart valve and the valve connection portion of the shaft to maintain the prosthetic heart valve in a radially compressed state and maintain the posts within the recesses. The delivery apparatus can cause relative axial motion between the delivery sheath and the valve.