Abstract <p>We consider the disintegration of material in cyclic conditions after extreme durations (10⁸–10¹⁰&#xa0;cycles). Traditional methods of fatigue testing are ineffective for such durations. A high-frequency test method based on the theory of nonsteady elastic vibrations in metals is proposed. The fundamental principles of the test method are outlined. A one-dimensional problem regarding steady vibrations in an isotropic elastic medium is formulated and solved. On the basis of the fundamental principles for steady vibration and the corresponding analytical solutions, the concept for cyclic fatigue testing at extreme duration is developed. Test methods and equipment are described. Finally, tests results for VT3-1 titanium alloy in cyclic fatigue after extreme durations are presented. They confirm the effectiveness of the proposed method for studying the cyclic failure of metals after extreme durations.</p>