This article deals with the numerical study of the singularities appearing in the spectral 3-D Green's function associated with the piezoelectric surface acoustic wave components (so-called SAW components). These electrical units are currently used today in several devices produced by the telecommunications industry (radio, TV, radar, and digital telecommunication systems). The need to improve their performance has motivated engineers and researchers to use mathematical modeling intensively, in particular the integral equations technique here used, which requires the computing of the associated Green's function and the study of its properties.