An analysis of PZT‐7A plates driven into thickness‐extensional trapped energy vibrations by the application of a voltage to strip electrodes and radiating into an adjacent fluid is performed. All previous treatments of thickness‐extensional trapped energy modes in piezoelectric plates have ignored the radiation into the surrounding medium and, hence, have been for resonators rather than transducers. The solution consists of a sum of a driven thickness solution and the pertinent plate eigensolutions for shorted electrodes in the electroded region and for zero surface charge in the unelectroded region, including in each instance the radiation into the adjacent fluid. Since the sum of the solutions in each region satisfies the differential equations and boundary conditions on the major surfaces including the fluid loading exactly, the substitution into the appropriate variational principle of linear piezoelectricity yields integral conditions across the thickness of the plate at the edge of the electrodes. The resulting system of inhomogeneous linear algebraic equations yields the response from very low frequency to slightly above the first thickness‐extensional frequency of the unelectroded plate.