Abstract: A flexible composite coupling (20) wherein a wound filament or roving is wound between two attachment members (22) and (24) and is fully or partially impregnated with a resin matrix such as urethane to form a flexible element (32). The attachment members (22) and (24) include radially extending flanges (26) and (28) which have a radiused periphery (30) formed on them, over which the flexible element (32) is wound. The flexible element (32) diverges inwardly from the flanges' (26) and (28) radiused periphery (30) to form opposed diaphragm portions (34) and (35) of the flexible element (32) which smoothly meet at a minimum diameter (36). Hoop winds (38) of a material with high strain capacity wrapped about this minimum diameter (36) pretension the filaments or roving within the flexible element (32).