A medical device assembly may include an elongated tubular membrane (20, 320, 420) having a wall (422) defining a lumen extending through the membrane from a proximal end to a distal end, the lumen having a first inner diameter, and a percutaneous medical device having a maximum outer diameter greater than the first inner diameter, wherein the membrane is configured to permit the medical device to pass through the lumen, and wherein the membrane includes a plurality of longitudinally-oriented channels (450) recessed along an inner surface of the wall. A medical device delivery sheath may include a tubular first layer (222) of polymeric material formed into a wavy cross-section having a plurality of lobes (230) and a plurality of valleys (240), wherein the first layer of material is resiliently expandable in a radial direction from a relaxed configuration to an expanded configuration, and wherein the first layer of material is substantially non-expandable in an axial direction.