The amplitude-dependent internal friction of continuously-cast and rolled AZ31 magnesium alloy was measured in this study. Samples were annealed and quenched step by step; immediately after the treatment, the amplitude dependence of the logarithmic decrement was measured. Changes in the microstructure due to thermomechanical treatment were reflected in changes in the damping. Internal friction is influenced by the dislocation substructure and its modification due to solute atoms migration, microplastic deformation, and twins’ formation. Internal friction in the rolled sheets is affected by the rolling texture.