There are various ringshaped automotive and machine parts and the study about the characteristics of ring are the important basis of the quality control and performance improvement of outer race of ball bearing, railwheel, ring gear, piston ring, and other ringshaped seals, etc. In this study, the effect of prestress which arise inevitably during the fitting of the ring shape parts and the effect of central line extension/contraction on the vibrational characteristics of ring are verified. Although many studies are made on the vibration of ring, the study about prestress and extension were rather scarce and rare. As a result of the study, a series of frequency formulas are derived. The result of this study can be utilized in the improvement of design as well as in the quality control during the fitting work.