Marine reduction gears are usually used to increase the propulsion efficiency of propellers for ships powered by medium and small sized high speed diesel engines. Most of shaft systems adopt flexible couplings to absorb the transmitted vibratory torque from the engines to the reduction gears and to prevent the chattering phenomenon of reduction gears. However some elastic couplings show non-linear characteristics due to the variable torque transmitted from the main engines and the change of ambient temperature. In this study dynamic characteristics of flexible couplings sare investigated and their effects upon various vibratory conditions of propulsion systems are clarified. A calculation program of torsional vibration for the propulsion systems are clarified. A calculation program of Results of the program developed are compared with ones of the existing linear method and propulsion systems with the elastic couplings the transfer matrix method is adopted which is found to give satisfied results.