The analysis of the exponential solid horn vibrating in the ultrasonic screw mode which can be utilized in machining, is described. The screw vibration can be produced by synthesizing longitudinal and torsional vibration. For an exponential horn to vibrate in screw mode, the horn must be shaped in specified dimensions, which is given by our calculation. The dimensions are determined by the taper constant of the horn, which is a function of the ratio of the resonance order of the torsional vibration to that of the longitudinal vibration. The results of the measurement with the horn designed according to the theory well supported the theory. The principal characteristics of the above horn are as follows : (1) The velocity of screw vibration distributes from large end to small end of the horn so that the direction of the velocity changes from half right, vertical, half left, horizontal and again half right in order, and the amplitude of the velocity gradually increases. (2) The nodal point do not exist in the distribution of the screw vibration. This seems to introduce troublesome problem in fixing the horn. The problem can practically be proved by binding the position of the smallest velocity amplitude near the large end of the horn with sponges, affecting little the vibration of the horn.