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The transmission of acoustic waves through a piezoelectric plate is dealt with theoretically and experimentally. The analytical treatment engages the octet formalism of anisotropic piezoacoustics. A specific version of the plate admittance matrix is introduced, which incorporates the electric boundary conditions for a non-metallized or metallized plate. In consequence, expressions for the reflection and transmission coefficients are reduced to explicitly the same form as in the case of pure elasticity. This theoretical model is then applied for material characterization. Material constants of a Pz27 plate are inferred from the numerical simulations and the experimental results of ultrasonic-transmission measurements. Good agreement is observed with another method based on electrical-impedance measurements. The impact of electrical boundary conditions is visualized by presenting the numerical and experimental transmission spectra through the Pz27 plate with non-metallized and metallized faces.