When the crankshaft of diesel engine has more than 3 throws, which are arranged in a different plane, its vibration induces coupled motions, especially the coupled torsional and axial vibration. Nowadays, the torsional vibration which is influenced rather weak than axial one, can be theoretically calculated fairly accurately, but theoretical calculation results of the axial vibration which is influenced strongly from torsional vibration is not so good. To get accurate calculation results of axial vibration, coupled axial-torsional vibration must be treated. In this investigation, coupled effects of vibration of diesel engine propulsion shafting are analyzed theoretically and some simple calculation methods are also studied. On this first report, effects of coupling on natural frequencies and their modes are mainly studied, setting the each mass in 4 degrees of freedom.