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In this article, piezoelectric ceramic is a core device of an ultrasonic wireless power transmission (UWPT) system. The most commonly used piezoelectric ceramic in research and applications of UWPT has a ring-like shape. The piezoelectric ceramic rings usually work in the presence of significant radial and axial vibrations as long as they are not extremely thin. However, in most studies related to the UWPT, only the axial vibration mode is considered. The Mason equivalent circuit model of axial vibration is widely used and the effect of radial vibration on the whole system is ignored. In this article, first, a method to analyze the piezoelectric ceramic ring considering the radial-axial coupled vibration is proposed. Second, the analytical expressions of the constitutive equations of the piezoelectric ceramic ring are derived. Third, a new form of analytical equations is constructed, and a novel two-dimensional equivalent circuit of the UWPT system considering the radial-axial coupled vibration of the piezoelectric ceramic ring is proposed. Fourth, the input and output characteristics of the proposed model and the conventional Mason equivalent circuit model are simulated using MATLAB. Last, the simulation results are compared and verified by experiments. The results demonstrate that the proposed model can describe the system resonance more accurately and comprehensively than the conventional Mason model. As a whole, this study increases the accuracy of the equivalent circuit model of the UWPT system and has important theoretical significance for UWPT research. [ABSTRACT FROM AUTHOR]