The invention relates to the field of turbomachines, and more specifically to an annular element (13) for a turbomachine casing, which has at least one inside face (14) defining a flow passage for a working fluid of the turbomachine, an outside face (15), and a damper (18), comprising at least one resilient coil turn (18a, 18b, 18c) fitted tightly around a surface of revolution (15a) of the outside face (15), in such a manner as to exert pressure on said surface of revolution (15a). The present invention also relates to damping a rotating wave of distortion of such an annular element (13) for a turbomachine casing, wherein said rotating wave is damped by friction between said surface of revolution (15a) and the at least one coil turn (18a, 18b, 18c) of the damper (18).