Piezoelectric stack actuators have great potential in structural vibration control and other applications, and it is critical to build a mathematic model that can depict important physical behavior of the actuators. An impedance-based model that can describe the electromechanical coupling characteristics of the actuators is developed in this paper. Short circuit mechanical impedance matrix, electric impedance and transduction coefficients are derived based on a rod model and the constitutive relationships of piezoelectric materials. Transduction equations in matrix form that represent the electric-mechanical interaction of the actuators are introduced by taking advantage of these three parameters. Numerical simulations are also conducted to verify the theoretical derivation. Both theoretical analysis and simulation results show that the impedances of external structures attached to the actuators have a significant influence on these parameters. The resonance frequency for the electric impedance and transduction coefficients is the highest when the two external impedances are exactly equal, and decreases for other cases. The influences of external impedances need to be considered to get a satisfactory control.