In turbo-machines such as a turbine and a compressor, the vibration of a rotor blade becomes a problem. The major cause is the resonance by fluid forces due to the viscous wake of the proceeding blade row and the use of a high damping material is effective to the protection. The material damping has usually been evaluated for only the first mode and the material damping of higher modes has been assumed to be the same as that of the first mode. This time the damping of various modes of the long blade could be obtained by using the rotating test rig. The result showed that the effect of vibration modes on the damping ability was small. This fact was verified by using the concept of the specific damping.