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An ultrasonic texture measurement system for sheet metal is being developed using rotating electromagnetic acoustic transducers (EMATs). We report on further investigations of deviation from theoretically predicted symmetries in the elastic constants (as measured ultrasonically using the aforementioned system) of cold-rolled aluminum sheet reported in earlier publications. A study of the effects of annealing and deliberate deformation (both elastic arid plastic) are used to develop an explanation of the nature and likely origin of this asymmetry. These deviations from symmetry cannot be detected by ultrasonic Lamb wave measurement in three directions alone. Texture asymmetry is relevant to the sheet metal manufacturer as it affects formability and may indicate processing problems. Results indicate that the asymmetry in the measured ultrasonic Lamb wave velocities on either side of the rolling direction is due to a stress effect rather than crystallographic texture.