This paper discusses the validity of (adaptive) Lagrange generalized plain finite element method(FEM) and plate element method for accurate analysis of acoustic waves in multi-layered piezoelectric structures with tiny interfaces between metal electrodes and surface mounted piezoelectric substrates. We have come to conclusion that the quantitative relationships between the acoustic and electric fields in a piezoelectric structure can be accurately determined through the proposed finite element methods. The higher-order Lagrange FEM proposed for dynamic piezoelectric computation is proved to be very accurate (prescribed relative error 0.02%-0.04%) and a great improvement in convergence accuracy over the higher order Mindlin plate element method for piezoelectric structural analysis due to the assumptions and corrections in the plate theories. The converged Lagrange finite element methods are compared with the plate element methods and the computed results are in good agreement with available exact and experimental data. The adaptive Lagrange finite element methods and a new FEA computer program developed for macro- and micro-scale analyses are reviewed, and recently extended with great potential to high-precision nano-scale analysis in this paper and the similarities between piezoelectric and seismic wave propagations in layered structures and plates are stressed.