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A fast and accurate method for analysis of surface acoustic wave diffraction is presented. The technique involves deriving asymptotic expansions for the diffracted beam profile (or frequency response) of a specified surface acoustic wave source, where the asymptotic expansion parameter is proportional to the distance to the observation point (or transducer separation). For moderate distances on the order of 25λ0, this method is more than 25 times faster than existing techniques using adaptive numerical integration schemes, and the speed advantage grows dramatically to well over 70 as the distance is increased to 100λ0. The accuracy is better than 1% for the 25λ0, distance, and also grows dramatically with increased distance. It is further observed that the asymptotic expansion is valid in the very near field region (distances on the order of 2.5λ0 ) with only a marginal loss in accuracy. These techniques can be applied to a wide class of highly anisotropic materials, and enjoy a significant computational speed and accuracy advantage over existing methods.