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A method to rapidly measure the group velocities (or their inverse, slownesses) of surface acoustic waves (SAWs) in anisotropic materials is presented. Surface acoustic waves are generated using a pulsed laser focused to a point on a test object. A newly developed multiplexed two-wave mixing (MTWM) interferometer is used to simultaneously detect the SAW displacements along eight different directions using a circular array of detection points. The group velocity slowness curve is obtained directly from the measured signals from the MTWM array. The experimental results are compared to theoretical predictions in aluminum, silicon, and quartz.