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Rubber materials have large deforming ability without damaging their internal structure. High damping rubber (HDR) is used in vibration isolator such as a rubber bearing for bridge etc. The mechanical behavior of HDR depends on strain rate, hysteresis, and temperture. The 3-parameter model generalized into the finite strain theory is used as constitutive model for HDR. It was attempted to observe hysteresis-dependent behavior of HDR experimentally to take this phenomena into a constitutive model. Finally, the hysteresis in rate-dependent behavior of HDR is not observed.