The present invention has for its object to provide a damping material which, despite a high damping capacity at and around room temperature, has a small temperature dependence of rigidity at and around room temperature and a damping material having hot-melt processability and a good balance between damping capacity and temperature dependence of rigidity at and around room temperature.This invention provides a damper material composition wherein the ratio of the storage modulus (G') value at 0.degree. C. to the corresponding value at 40.degree. C. as found by the measurement of dynamic viscoelasticity in the shear mode, namely (G'.sub.0.degree. C./G'.sub.40.degree. C.), is not greater than 15 and the loss tangent (tan .delta.) value as found by said measurement is not smaller than 0.4 at 0.degree. C. to 40.degree. C.