Abstract: So far, the diffracted SAW field generated by an IDT with finite aperture on a piezoelectric crystal surface is usually analyzed phenomenologically by angular spectrum theory. The main approximation of this scalar theory is ignoring the vector nature of the field and assuming that the wave field can be represented by a scalar as in optics. In this paper, the rigorous vector theory developed previously of the surface excitation of elastic wave field in piezoelectric crystal is used to obtain the SAW diffraction field strictly. As an example, numerical results for YZ-LiNbO₃ are calculated and compared with those obtained from angular spectrum theory.