Until recently, the calculation of torsional vibration for the marine diesel engine shafting has been performed only for vibratory stresses of resonant points and vibratory stresses for other engine speeds are determined by the estimation. With the advent of energy-saving engines which have a long stroke and a small number of cylinders, the first major critical torsional vibration of the propulsion shaft appears ordinarily near the MCR speed of engine and the flank of its vibratory stress exceeds now and then the limit stress defined by the rules of Classification Society. In order to know the above condition in the design stage of propulsion shafting, it is necessary to calculate the forced torsional vibration with the damping of propulsion shafting for all orders and to synthesize its calculated results according to their phase angles. In this study, the forced torsional vibrations with the damping of propulsion shafting are calculated for several orders by mechanical impedance method, and their results are synthesized. A computer program for above calculations are developed and some test-runs of the developed program are performed for propulsion shaftings of actual ships. The results of calculations are compared with measured values and also with those of the modal analysis method. They show fairly good agreements and the developed program is checked up on its reliability.