Recently, multi-branced driving systems are often used for power station systems or for marine propulsion systems to save the initial cost, the man power and to improve the energy efficiency. As the multi-branched power system has a very complicated vibrating system, its analyzing method is quite different from the ordinary method for the single straight system. In this study, the multi-branched power system is reduced to derive equations of free vibration and some analytical methods are studied to solve these equations and computer programs are developed to calcuate their numerical solutions. And also, equations of forced-damped vibration of the multi-branched power system which involves diesel engines are derived and their solving methods are studied. Some computer programs are developed to get responses of the forced vibration with damping and their results are synthesized to get resultant responses. Finally, exciting forces of diesel engine and damping forces of power driving systems are appreciated to help field engineers by suggesting reasonable method of estimating their values.