This chapter is concerned with self-excited bending vibration of high-speed rotating shafts. Internal friction destabilizes such systems, thus its presence plays a definitely different role with respect to its effect on bending vibration of beams or torsional vibration of shafts. Rotating shafts, even if perfectly balanced, exhibit self-excited vibration brought about by internal energy dissipation. The loading stabilizes the shaft with progressive elastic characteristics. Degressive characteristics can lead to bifurcation appearing at a lower angular velocity. Internal damping in a rotating shaft is the source of non-conservative forces which can convert the energy of rotary motion into transverse vibration energy. It results in a dynamic instability of the static equilibrium position of the shaft at higher rotation speeds. Transverse loading can either stabilize or destabilize the system, depending on the sign of the material non-linearity. Strongly loaded shafts exhibit amplitude hysteresis even for a progressive material non-linearity.