A delivery system for delivering a collapsible prosthetic heart valve includes a valve support structure for supporting a collapsible prosthetic heart valve, and a distal sheath movable in a longitudinal direction relative to the valve support structure between a first position in which the distal sheath is adapted to surround a collapsible prosthetic heart valve supported on the valve support structure, and a second position in which the distal sheath is adapted to expose the collapsible prosthetic heart valve for deployment. The distal sheath is at least partially formed of an inner polymer layer, an outer polymer layer, and a tubular supporting member sandwiched between the inner polymer layer and the outer polymer layer.