An analysis of PZT‐7A plates driven into thickness‐extensional trapped energy vibrations by the application of a voltage to strip electrodes is performed. The plate waves in the unelectroded region that carry energy away from the trapped mode are included in the treatment. The solution consists of a sum of the driven thickness solution and the pertinent plate eigensolutions for shorted electrodes in the electroded region and for zero surface charge in the unelectroded region. Since the sum of the solutions in each region satisfies the differential equations and boundary conditions on the major surfaces 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.