A multi-junction, multi-branch torsional vibration system is often found in a geared rotating system. This is an important part in many types of machinery, such as mining machinery, petroleum machinery, steel rolling machinery and automobiles. If the design parameters of the system are improper, there will be serious torsional vibration, which will cause noticeable sound disturbances, severe shakings, and component fatigue problems. Analyzing and pre-estimating critical speeds or torsional natural frequencies and mode shapes of the vibration systems in the design stage is very important to avoid future disastrous and costly repairs of the machinery. In this paper, a radical and effective method for calculating natural frequencies and mode shapes of multi-junction, multi-branch torsional vibration systems, has been put forward, a program named MJBTVAP (Multi-Junction, multi-Branch Torsional Vibration Analysis Program) based on this method has been developed, actual problems have been solved.