While designing a torsional shafting with various gear-branched systems, it is very important for system designers to obtain critical speeds accurately and easily. The author has studied the transfer stiffness coefficient method (TSCM) as a structural analysis algorithm. In this paper, the TSCM is applied to the computation of critical speeds for torsional shafting with gear-branched systems. The accuracy of the present method is confirmed by comparing with the results of the finite element method.