The torsible, flexible linking arm with integrated flexion damping according to the invention includes, between two rigid end portions, a flexible central portion constituted by a peripheral bundle (6) of rods (8) of fibres with high mechanical strength encapsulated in a flexible, vulcanized elastomer (9), and by a central damping core (7) with a strip (13) shearing a damping gel (12) filling a tight, flexible bladder (11) embedded in the elastomer (9). When deformations occur in the plane of the strip (13), the latter shears the gel (12), which produces damping that is added to that resulting from the deformation remanence of the elastomer (9). Application to the linking of two rigid bodies such as a rotor blade and its hub.