A delivery assembly comprises a delivery apparatus and a prosthetic valve releasably connected to a cord-retaining device of the delivery apparatus by a plurality of cords or tethers. The cords desirably have a multi-stranded construction formed from a plurality of strands of material. The multi-stranded construction can be, for example, a braided construction, a twisted construction, or a whip-stitch construction. The multi-stranded construction can include integral openings along opposing end portions of each cord. Each cord can extend through an aperture in an apex of the frame of the prosthetic valve or around an apex with one end portion of the cord being retained on the cord-retaining device and another end portion of the cord being retained on a slideable release member of the delivery apparatus.