Theoritical formulas for desingning an exponentional or conical horn for longitudinal or torsional vibration in ultrasonic cutting are established in this report. Then, the mechanism of the tool post that is much important for developing the fundamental research or effective application to various cutting tools is investigated. And it has been found that the structure of an ultrasonically vibrated cutting tool calculated by these formulas has a style suitable to coventional machine tools and has several nodes. An ultrasonically vibrated cutting tool can be fixed statically on the machine tool by supporting these nodal points.