In this paper, the concept of electrical effective permittivity function is used to calculate the eigen-frequencies and the particle displacements of piezoelectric acoustic plate modes (APM). These results allowed us to determine the mass sensitivities of the first order vibration modes using a first order perturbation theory. Theoretical results are discussed and compared to those of a variational method and isotropic two-layer composite analysis in the case of a shear horizontal APM sensor on a singly rotated cut quartz substrate. Experimental measurements by a copper electrodeposition are carried out and show that the perturbation method leads to a better understanding of the APM behavior.