In this paper, we investigate numerically the coupling of the Rayleigh mode with the micro-wall resonance modes in inter-digital transducers (IDTs) electrodes of surface acoustic wave (SAW) devices. We perform a finite element analysis (FEA) of the SAW features using an implemented model using COMSOL Multiphysics® software. The SAW structure comprises identical transmitter and receiver IDTs electrodes, with different electrode heights (he). The proposed FEA study is based on the extraction of reflection (S11) and transmission (S21) coefficients of the SAW device. The IDTs are considered to be a micro-wall phononic crystal acting as local resonators at frequencies inside the SAW passband. The locally resonance gap is strongly dependent on the he value, S11 and S21 parameters are affected by the SAW energy absorption in the IDTs system. We have chosen two he values (0.5 and 3 µm) to study low and high aspect ratios of micro-walls; corresponding respectively to Bragg-type and resonance-type bandgaps appearing near to the SAW central frequency. At the SAW resonance frequency, the return (S11) and the insertion (S21) losses are reduced. S21 is reduced by 12.73 and 18.49 dB for he=0.5 and 3 µm, respectively, accompanied by an increase in the quality factor, and S11 parameter is reduced by 1.357 and 4.98 dB for he=0.5 and 3 µm, respectively.