This paper develops an analytical 3D model of ultrasonic welding transducers. The presented model investigates the effects of the workpiece's stiffness and material properties on transducers' frequency response and mode shape. Longitudinal and lateral vibration is taken into account in the model. In order to analyze the forced vibration of the transducer, the effect of piezoelectric and excitation electrical fields are considered. The structural damping is considered as an imaginary Young's modulus. For validation of the model, a transducer, booster, and horn with specific dimensions and physical properties is modeled in ANSYS software. Its resonant frequency is compared with the mathematical model. Then, the system is fabricated for experimental tests. The resonant frequency in the analytical model, simulation, and the experimental test is achieved, 19208 Hz, 19280 Hz, and 19203 Hz, respectively. There is a 0.02% error between the analytical model and the experimental test. The Anti-resonant frequency in the analytical model is 19265 Hz which has a 0.02% error with experiment (19270 Hz). The admittance at a resonant frequency in the analytical model is 0.01755 mS which has a 0.2% error with the experiment (0.0176 mS). The mechanical quality factor of the transducer and its vibration amplitude are calculated by the developed analytical model according to the mechanical properties of components.