There is now a rich variety of piezoelectric materials available for surface acoustic wave applications. These include crystals in symmetry classes mm2, 32, 3m, 4mm, 6mm, and 4a3m. Classes 6mm and 4a3m include most of the binary semiconductors, such as gallium arsenide and related alloys, making integrated acoustic/electronic devices possible. Depending upon use, the SAW substrate material may be chosen to have certain combinations: piezocoupling, temperature coefficient of frequency or delay, small coupling to bulk modes, low sensitivity to acceleration or thermal transients, high acoustic Q, small power flow angle, etc. In this paper, these and other criteria are discussed broadly, with illustrations of pertinent materials and orientations. Also given are recommendations of substances for which the material constants are well enough known to be practical, as well as indications for necessary future work in growth and characterization. A broadband equivalent electrical network for SAW propagation is presented, by means of which the appropriate material parameters may be extracted from network analyzer measurements. The circuit can also serve to represent the salient features of devices in their working environments.