The one-dimensional vibration mode of a piezoelectric layer under different load conditions has been reconsidered. Derived analytical expressions for admittance and impedance at special frequencies are listed. Based on the expressions derived, two applications are proposed involving electrical measurements on a piezoelectric plate. Concerned are first the determination of such plate material parameters which are relevant for its thickness mode of vibration. Difficulties due to spurious vibration modes are avoided in this approach. The second application deals with an alternative determination of acoustic material-impedances otherwise not easily obtainable: a piezoelectric plate is coupled to the material surface by a liquid. The influence of the coupling layer thickness is discussed and a measurement procedure is given by which the detrimental layer thickness effect is minimized.