Abstract: A reversible endless belt rotary coupling particularly suited for use in connecting a drive shaft and driven shaft permitting the driven shaft to rotate in either, rotational direction and to rotate about an axis that may be angularly misaligned with respect to the rotational axis of the drive shaft. The coupling includes a series of preloaded endless belts embedded in an elastomer matrix material, arranged tangentially with respect to the connected shafts and connected thereto by bobbin-like spools at the ends of the belts. The endless belts are axially stiff to accommodate tensile and compression loads and are flexibly and torsionally soft to accommodate the motion while transferring torque between the drive and driven shaft.