In this paper, the wave reflection and transmission characteristics of an axially strained, rotating Timoshenko shaft under general support and boundary conditions, and with geometric discontinuities are examined. As a continuation to Part I of this paper (Kang and Tan, 1997), the wave reflection and transmission at point supports with finite translational and rotational constraints are further discussed. The reflection and transmission matrices for incident waves upon general supports and geometric discontinuities are derived. These matrices are combined, with the aid of the transfer matrix method, to provide a concise and systematic approach for the free vibration analysis of multi-span rotating shafts with general boundary conditions. Results on the wave reflection and transmission coefficients are presented for both the Timoshenko and the Euler-Bernoulli models to investigate the effects of the axial strain, shaft rotation speed, shear and rotary inertia.