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A three-dimensional (3D) model of a high-power ultrasonic, composite, unidirectional transducer is proposed in this paper. The proposed 3D Matlab/Simulink model of the composite transducers predicts the thickness and the radial modes of oscillation as well as their mutual couplings. This longitudinal, prestressed, asymmetrical, piezoelectric transducer, which consists of two active piezoelectric layers, front, back and central oscillating metal mass, is realized. Due to its special structure, the central mass is not bounded using a bolt and performs unidirectional piston motion as compression and expansion occur in cycles keeping the axial dimension of the transducer roughly constant because of mutually opposite polarization of active elements. The electromechanical equivalent circuit of the transducer, representing one-dimensional (1D) model, is derived first and is also presented in this paper, while the resonance frequency equation is obtained analytically. Few composite transducers are designed and manufactured. Their resonance frequencies are measured and compared with the analytically obtained results for a large number of electrical connection combinations. In order to demonstrate the capabilities and limitations of the 1D model, comparison with the results from the 3D model are made. Results show that the measured frequencies are in good correspondence with the analytically obtained from 1D model only for the thickness modes and from the 3D model for the thickness and the radial modes of oscillation and their mutual coupling.