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Torsional vibration usually causes noticeable sound disturbances, mechanical shakings, and component fatigue problems. It exists at one or more periods of the operating range in torsional systems. Determination of critical speeds or torsional natural frequencies in a design stage makes it possible to avoid early fractures and costly repairs of the machinery. In this paper, the method for predicting speed–related excitation frequencies of complex rotating systems is discussed and the computer program is developed and tested by actual examples. The natural frequencies and mode shapes of multi–branch torsional vibration systems with one or more junction points are calculated. A user–friendly graphic interface for modeling is presented. Some practical examples are given and the results of the simulations are compared to those obtained analytically as well as those given in references.