A conventional packing ring was designed with a large clearance to prevent damage due to the vibration of the rotor, which can lead to an increase in steam leakage. In this study, a flexible packing ring using winding springs was developed to prevent damage to the rotor teeth by minimizing vibration, while maintaining a smaller clearance than that of conventional rotor designs. Theoretical analysis and finite element analysis (FEA) were used to design the winding spring to satisfy the specified allowable stress limit and minimum load requirements. The shape of the winding spring was designed by applying curves to the center and end parts of a flat spring. Computational fluid dynamics (CFD) analysis was used to predict the leakage of the flexible packing ring. Flow rate measurement tests were performed to verify the leakage reduction efficiency and the reliability of the CFD analysis.