In this paper, transverse waves propagating in an infinitely long, rotating Timoshenko shaft subjected to axial forces are studied. The model includes the contributions of axial deformation to the transverse vibration of the rotating shaft. Four different types of wave motions, two cutoff frequencies and frequency spectra are defined and discussed. The wave reflection and transmission characteristics of the shaft at arbitrary point supports are also examined by deriving the reflection and transmission matrices for an incident waves upon a general intermediate support. Numerical results showing the effects of axial force, shaft rotation speed, shear deformation, and rotary inertia on the wave reflection and transmission coefficients for classical supports are presented for both the Timoshenko and Euler-Bernoulli beams. It is found that the wave motions are generally independent of the rotation speed and the axial load affects significantly the wave motions at small real wavenumbers.