In this chapter, the fundamental differential equations of piezoelectric bending transducers are derived from the extended Hamilton principle for non-conservative systems. The Lagrange function required for this is derived from the electrical enthalpy density, which has already been derived from the equations of state for piezoelectric materials in Chap. 7. The application of a position and time dependent line load to a piezoelectric layer system is the starting point for the calculation of the work of non-conservative quantities. The subsequent variation of the Lagrange function as well as the variation of the external work of the non-conservative quantities leads to the required differential equations based on the extended Hamilton principle.