A vibration-proof damping polymer material characterized in that the material is prepared from a polymer substance obtained by dissolving an amorphous fluorine-containing polymer in an acrylic monomer and polymerizing the monomer with or without permitting the resulting polymer to form an interpenetrating polymer network, and a vibration-proof damping polymer material characterized in that the material is prepared from a blend of (a) and (b), (a) being an amorphous fluorine-containing polymer or crystalline polymer containing vinylidene fluoride, and (b) being an acrylic polymer.