Torsional rotor vibration (TRV) is angular vibratory twisting of a rotor about its centerline superimposed on its angular spin velocity. TRV analysis is not needed for many types of rotating machinery, particularly those machines with a single uncoupled rotor. Many single-drive-line rotors are stiff enough in torsion so that torsional natural frequencies are sufficiently high to avoid forced resonance by the time-varying torque components transmitted in the rotor. A notable exception is the quite long rigidly coupled rotors in modern large steam turbine generator sets, examined later in this chapter. When single rotors are coupled together, the possibility is greater for excitation of coupled-system torsional natural frequency modes. Coupling of single rotors in this context can also be through standard so-called flexible couplings connecting coaxial rotors and/or through gears. In most coupled drive trains, it is the characteristics of the couplings, gear trains, and electric motors or generators that instigate TRV problems.