The purpose of this article is to investigate the properties of surface acoustic wave (SAW) propagation using the finite element method (FEM). The results compare with the well-developed couple-of-mode (COM) theory and other literatures in order to check the accuracy and feasibility of the model that we build. The effects of piezoelectric substrate and electrode geometry will take into account not only to examine the model but also to acquire the helpful information to design the SAW filter and reflector. Via the suitable modeling, mesh modulate, and the correct boundary condition, we can obtain the results similar to those works by COM theory. All results in this article show clearly that this FEM model is suitable to predict the SAW behaviors, moreover, we can simulate the more complex condition, i.e. sensor capability, temperature coefficient, multi-layer structure, impedance response, scattering parameter and so on.