A novel mode of ultrasonic oscillation is generated in a Langevin ultrasonic transducer comprising a metal block, a metal block provided with a supporting means protruding in a ring shape on its side surface, and polarized piezoelectric elements fixed between these metal blocks, by connecting the ultrasonic transducer to a base via the supporting means, whereby supporting the ultrasonic transducer on the base in a restrained state, and applying to the piezoelectric elements a voltage having such frequency that the ultrasonic transducer generates an ultrasonic oscillation with back-and-forth motion in a direction perpendicular to plane surfaces of the piezoelectric elements which has no oscillation node within the ultrasonic transducer; this novel ultrasonic oscillation mode is utilized for performing ultrasonic machining methods as well as for ultrasonic transmission method.