Abstract: A torsional vibration monitoring system for monitoring torsional vibration occurring in a rotating shaft system such as in a power generator turbine is disclosed. Torsional vibrations are measured at a small number of measurable positions on the rotating shaft system, and stresses at other arbitrary positions are estimated by linearly decomposing the torsional vibrations. The fatigue life expenditure on the rotating shaft system is obtained and monitored on the basis of the estimation obtained by the linear decomposition of the torsional vibration. For a huge vibration such as caused by thunder which may produce stresses on the rotating shaft system and which can not be estimated by the linear decomposition thereof, the torsional vibration monitoring apparatus may be provided with means to produce data which may be used in other analysis, by recording real torsional vibrations caused thereby.