The paper deals with design, modelling, and testing of an ultrasonic (US) chain with torsional vibrations that includes a tool at its end and could be used for different industrial applications such conventional and nonconventional machining of revolution, helicoidal, and curved surfaces or various types of materials. The US chain includes a horn with helicoidal channel whose profile was studied aiming at growing the amplification of amplitude of the tool, positioned in an antinode point. After the shape design of US horn, finite element analysis was applied to simulate the torsional vibrations of the horn and integrated tool with highest amplitude. Some experiments were made at electrical discharge machining (EDM) aided by torsional ultrasonic vibrations. The results emphasized the technological parameters improvement like machining rate increase and surface roughness decrease, compared to usual EDM without US.