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Powertrain torsional vibration has become a subject of increasing concern for the heavy duty truck industry in recent years. This is due in part to truck and diesel engine developments, and to drivetrain system trends. A computer simulation is an effective tool in analyzing this problem. A powertrain vibration analysis program has been developed by the authors. It has been used extensively in the evaluation and optimization of powertrain system performance. In this paper, first the heavy duty powertrain is characterized as a vibrating system. Its natural frequencies, mode shapes and frequency response characteristics are reviewed. Second, the theory of torsional vibration and its application in the simulation are described. The drivetrain is described as a discreet model. An undamped modal analysis is given as an eigenvalue problem.