The present disclosure relates to a grinding machine. More particularly, the present disclosure relates to a centerless grinding machine comprising a damping device. The present disclosure also relates to a spindle for a grinding machine, and to a damping device for a spindle of a grinding machine, particularly for a grinding spindle or regulator spindle of a centerless grinding machine, wherein the damping device comprises at least one damping unit including an auxiliary mass section, an elastic section and a damping section, which are integrated in the spindle, and which jointly define a damped vibratory system for increasing the dynamic stiffness of the spindle.