A rotary flexible shaft for coupling between driving and driven member having female couplings has ends of noncircular cross-section. A strand of compressible material such as flocked yarn is helically wrapped around each end so as to leave spaces between turns which expose portions of the lateral surfaces of the ends. A coating of a silicone adhesive or other elastomer, or of a highly ductile material such as polytetrafluoroethylene, covers and is adherent to the strands and the exposed portions of the lateral surfaces of the shaft ends. Instead of a strand, the compressible material may constitute spaced ridges, islands, and/or protuberances adhering to the shaft ends.