Abstract: A tubular ultrasonic vibrational system with a conical varying cross-sectional area is designed.It is composed of a sandwich piezoelectric transducer and of a tubular ultrasonic resonator with the conical varying cross-sectional area.The equivalent circuit of the tubular ultrasonic vibrational system is deduced and the resonance/anti-resonance frequency equations are obtained.The vibrational system is analyzed and designed by the equivalent circuit method and the finite element method,an experimental prototype is also manufactured.The results show that the equivalent circuit of the tubular ultrasonic resonator is a novel non-reciprocal two-port equivalent network,and the tubular ultrasonic vibrational system has a good vibrational performance:better isolation of the operating frequency from close non-tuned modes,uniformity of amplitude at the working surface and high amplitude of the operating mode.It is expected to be used in some ultrasonic applications,such as continuous seam welding of plastic sheet or strips,ultrasonic cutting of a ring-type plastic element and ultrasonic drilling,etc.