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One of the elements of tire stiffness is sidewall stiffness. This stiffness, which influences tire vibration characteristics, is also an important design parameter for carrying the vehicle body. Tire is one of pressure vessels and inflation pressure is dominant in sidewall stiffness. Thus, tire sidewall stiffness is decided from the tension of inflation pressure and the structural dynamic, including the properties of the rubber material. To reveal the dynamic characteristics of tire sidewall stiffness, this study describes differences in stiffness due to inflation pressure. It can be expected that variation of inflation pressure is monitored from the axle vibration response during vehicle traveling in the future. That is because the relationship of the vibration characteristics and the inflation pressure of tire are derived by sidewall stiffness. First, we derive a formula for sidewall stiffness based on the structural dynamics of Akasaka's theory.