It is very important to analyze the torsional vibration for the propulsion shafting of ship. The authors have developed the transfer stiffness coefficient method(TSCM) as a vibration analysis algorithm. The concept of the TSCM is based on the successive transfer of stiffness coefficient. The effectiveness of the TSCM was verified through many applications. In this paper, the TSCM is applied to the torsional free vibration analysis for the propulsion shafting of an actual shin with a diesel engine. In order to calculate the additional torsional stresses of the propulsion shafting the torsional forced vibration for the shafting is analyzed by using both the modal analysis method and the results of the torsional free vibration analysis by the TSCM. The accuracy of the present method is confirmed by comparing with the vibration analysis results of engine maker.