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Neutron diffraction has been used to measure the crystallite orientation distribution function for a cubic test sample of highly textured austenitic weld material. The longitudinal and transverse ultrasonic velocities in three orthogonal directions in the sample have been calculated from this function and compared with measured values for the sample. The Voigt approximation is found to give good agreement with experiment and appears to be the most useful approach for the calculation of ultrasonic velocities in highly textured materials.