A constraint type vibration damping material, which exhibits a high vibration damping performance and can realize easiness of processing and a low cost at the same time, is provided, in which a polymer viscoelastic layer made of rubber, etc. is formed on at least one surface of a rigid body such as a metal plate, etc. and a hard cover layer having a rigidity modulus greater than that of the viscoelastic layer and smaller than that of the rigid body. Since the hard cover layer having a great rigidity modulus acts as a constraining material, which forms as the result a pair with the rigid body. Further, since the polymer viscoelastic layer and the hard cover layer can be formed by continuous fabrication steps, it can be advantageous from the point of view of the cost.