The marine geared diesel propulsion systems are becoming extremely complex, with the increasing adoption of such arrangements as multi-drive systems and main engine driven auxiliaries, and the incorporation of such elements as highly damped flexible couplings and dampers. The article presents an analysis performed on digital computor concerning the steady-state forced torsional vibration in a multi-mass-elastic, multi-branch linear vibratory system with damping. The damping was considered individually for each machine element, and phasing was taken into account in the culculations which extended over the entire range of service speed. Some examples of calculation are given together with results of measurement, covering cases of geared diesel shafting systems equiped with either Geislinger flexible coupling or hydraulic coupling. It was found that the Geislinger coupling has distinct damping effect, the aspects of vibration differing in consequence quite markedly from undamped vibration. The hydraulic coupling was treated as part of an integral shafting between engine and propeller by the introduction of a spring constant representing the coupling, and the calculations proved that a vibration was induced on the intermediate shaft by the engine, this was substantiated by actual measurements. Accumulation of similar results of analysis should contribute to gaining a better knowledge of the damping in machine elements.