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The article focuses on the analysis of the internal damping changes depending on the amplitude of the magnesium alloy AZ31. Internal damping reflects the ability of the material irreversibly dissipating mechanical energy oscillations. It means that the material of high internal damping ability is able to significantly reduce the vibration amplitude. Internal damping is, generally, dependent on many factors (temperature, material purity, grain size, mechanical and thermal processing, etc.) and its value is determined by interactions between various mechanisms dissipation of mechanical energy. Ultrasonic resonance method was used in experimental measurements, which is based on continuous excitation of oscillations of the specimen, and the entire apparatus vibrates at a frequency which is near to the resonance. Starting resonance frequency for all measurements was about f = 20470 Hz.