Piezoelectric transducers (sensors and actuators) are widely used to produce motion or to sense displacement. One of the most applicable types of the piezo-electric transducers is a transducer in which the piezo stacks are sandwiched between two vibrating masses by a connecting stud. These types of the piezo-electric transducers which are utilized for sensing applications are known as Tonpilz. A piezo-electric transducer is usually designed to work in the resonant frequency, and modeling and simulating its dynamics behavior to check the desired performance are very important. In this study, by considering the concept of the admittance expression, the dynamics model of a piezo-electric transducer is derived, and based on it, the characteristics of the longitudinal vibration of the piezo-electric transducer are calculated. The admittance expression is in the matrix notation which contains the equivalent admittance matrices correspond to the various composing parts of the transducer. The matrix notation provides a flexible and simple way for modeling the piezo-electric transducer, by combining the various containing parts of the piezo-electric transducers. To calculate the equivalent admittance matrix, at first, the equivalent admittance matrices of the metallic and piezo-electric parts of the transducer are derived, and then they are collected in one matrix diagonally. Then, by applying the boundary conditions via matrix operations, the equivalent admittance matrix of the transducer is obtained. One of the benefits of this modeling is obtaining the optimal design by considering different parameters. At last, the obtained analytic model is verified by experimental measurements of some fabricated transducers, which shows a good agreement. © 2018 Elsevier B.V.