Optimization methods are used to find areas of maximum disagreement between the failure criteria of Tsai and Hart-Smith. The Tsai criterion is quadratic in the stresses and employs a selective and progressive ply-by-ply degradation scheme to predict ultimate load. Hart-Smith’s criterion is based on a fiber shear failure of the fibers and also predicts ultimate load. Both compression-compression and tension-shear combinations are identified as areas of large difference in predicted failure loads. Graphite-epoxy specimens are designed to maximize the difference in the failure loads computed from the two criteria under uniaxial tension. Both on-axis and ten-degree off-axis specimens are designed and tested. The laminates that maximize the difference in these criteria exploit the manner in which they treat the effect of in-plane shear on the failure prediction. Test results indicate little difference in the failure prediction for the on-axis test. However, the off-axis tests show that the Tsai criterion predicts failure much closer to the test results.