The reliability of propulsion shafting systems is a major concern for ocean-going vessels because mid-ocean repairs can be time-consuming and spare parts must be available. To address this concern, vibration modeling and experimental measurements were conducted on a propulsion shafting system with a Z-drive propeller, with the objective of identifying the source of failure for the flexible rubber coupling connecting the diesel engine with the intermediate shaft. The torsional fluctuations in the flexible coupling dramatically increased and then abruptly ceased. The modeling results revealed that the frictional losses during power transmission through the universal joints could act as an excitation force for self-excited vibration. The coupling connected to the intermediate shaft did not have sufficient radial flexibility to dampen these vibrations. To avoid the effects of the self-excited torsional vibration, it is recommended that this coupling is replaced with one that is capable of absorbing the radial shaft displacement.