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The problem of torsional vibration of the crankshaft of high speed diesel engine has become critical with increase in exciting forces due to high combustion pressures. This results in high torsional vibration amplitudes and hence high stresses. In such a case use of the damper pulley to control the torsional vibration amplitudes and stresses is one of the desired solution. In this paper torsional vibration analysis is carried out in case of six cylinder diesel engine using standard general purpose finite element package ANSYS and a method is developed to find out torsional vibration stresses leading to the selection of damper.