A multilayer casing device for attenuating electromagnetic waves is made of at least one textile material, at least one metal material. The device is made up of a stack provided with at least, consecutively from the inside to the outside: a first diamagnetic metal material layer at least partially made of copper, a second textile layer at least partially made of wool or cotton, a third layer made of a ferromagnetic material, and a fourth textile layer at least partially made of wool and cotton. The device is also made up of a complementary stack of identical layers (the second textile layer, the third ferromagnetic layer and the fourth textile layer) extending symmetrically in relation to the first copper layer.