The radial vibration of an annular ultrasonic concentrator with edge section is studied. Based on the electromechanical analogy, the radial equivalent circuit and the frequency equation of the concentrator are derived, the radial displacement amplitude magnification and the nodal circle equation are given. The relationship between the radial displacement amplitude magnification and radius ratio of the annular vibrator at the first and second order vibration mode is obtained. The relationship between the first and the second order radial resonance frequencies and the radius ratio of the annular edge section concentrator is analyzed. The displacement amplitude magnification of the annular vibrator at the second order resonance is lager than that of the first order vibration mode. Especially, when the radius ratio tends to one, the second order resonance frequency of the annular vibrator tends toward infinity. It can be concluded that there is no higher order vibration mode for a thin-walled circular ring. Furthermore, the experimental results show that the theoretical resonance frequencies and the amplitude magnification are in good agreement with the measured results.