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Knock noise induced by automotive shock absorbers has serious influence on driving comfort and vehicle quality. Some research focusing on knock noise had been introduced in the past. However there is the unidentified phenomenon that has been unnoticed. This paper describes the new theory to clarify one of the unidentified phenomenon and proposes the equation for stability assessment which is useful on designing stage of development. First of all, the characteristics of the unidentified rod vibration of shock absorbers are investigated experimentally. Second, the new theory is established on the basis of the non-linear physical model with friction forces between piston and cylinder. This theory shows that the unstable vibration, so called the Self Excited Vibration, can be induced by not only friction property but also structure of rod and piston. Third, the equation for stability assessment, which is useful on designing stage of development, is proposed on the basis of new theory.