This paper is focused on evaluation methods for materials at high amplitudes of ultrasonic vibrations. First, basic concepts on piezoelectric ultrasonic transducers utilized in power applications are introduced as well as horns and vibration converters. Second, an electrical equivalent circuit model of piezoelectric transducers is described. Then, a standard method to measure the output acoustic power of ultrasonic transducer is demonstrated. Third, the electromechanical coupling factor and quality factor are defined. The last half of this paper is dedicated to the transient method and quality factor measurement under high vibration strain. The quality factor and piezoelectric constant of piezoelectric ceramics are discussed as functions of vibration strain with the transient method. Next, an evaluation method for the quality factor of non-piezoelectric materials is proposed on the basis of the definition of quality factor. Ultrasonic characteristics of several metals and polymers are explored using the proposed method.