The purpose of this study is to determine the stiffness of rubber of dynamic damper. This damper system reduces the steering wheel vibration caused by idling oscillation of the engine. Therefore, in order to measure the stiffness of the silicone rubber in the dynamic damper system, the material test of the silicone rubber was carried out. Using the measured stiffness, the FEM model of the dynamic damper system was constructed and the correlation by the experimental data was shown at an error of less than 2%. In addition, the dynamic damper system was simplified to a two-degree-of-freedom spring-mass model and the effect of the stiffness change of the rubber on the natural frequency of the column shaft was analyzed theoretically. As a result, the amplitude of the column shaft was reduced as the stiffness of the silicone rubber was lowered.