Body noise or mechanical vibrations are damped by a sound or noise dampingovering that may be secured permanently or temperarily to the surfaces of a body to be damped in the manner of an adhesive tape. The tape or band type damping covering comprises two layers of platelet elements of highly elastic material interconnected with play, for example by hooks. The layers are so arranged that the platelet elements in one layer are staggered relative to the platelet elements in the other layer. An intermediate layer of a plastic type material is interposed between the two outer platelet layers. The plastic material converts shearing stresses and hence the vibrations into heat. The plastic material may be a gel which absorbs liquid.