According to the invention, there is provided a damping structure capable of obtaining a sufficient damping effect even against vibrations of small amplitudes, by promoting movements of powder/particle materials inside a hollow body. In the damping structure of the invention, a damping member 2 is provided on a structure 1 to be damped. The damping member 2 includes a hollow body 5 which is filled with powder/particle materials 3, partially leaving a space 4. A vibration wall face part 7 which vibrates more violently than the structure 1, on receiving vibration, is formed in at least a part of wall face parts 6 of the hollow body 5. The vibration wall face part 7 is preferably formed of a material having a lower elastic modulus and/or a lower density than the other parts.