Ice cores from Byrd Station and Little America V were used to test an ultrasonic technique for evaluating crystal anisotropy in the Antarctic Ice Sheet. P wave velocities measured parallel (Vp↓) and perpendicular (Vp→) to the vertical axes of cores from the 2164-m-thick ice sheet at Byrd Station yielded results in excellent agreement with the observed c axis fabric profile (Gow and Williamson, 1976) and with the in situ P wave velocity profile measured parallel to the borehole axis by Bentley (1972). Velocity differences of ΔV in excess of 140 m/s for core samples from deeper than 1300 m attest to the strong single-pole clustering of crystallographic c axes about the vertical, especially in the zone from 1300 to 1800 m. Such oriented structure is compatible only with strong horizontal shearing in this zone. The existence in an ice sheet of widespread shearing several hundred meters above its bed raises serious questions as to the validity of current concepts of the flow of large ice masses that tend to gloss over or ignore crystal alignments of this magnitude. In ice cores from the bottom 350 m at Byrd Station, the crystals are so large (up to 30 cm2 in cross-sectional area) that samples used for ultrasonic measurements usually contained too few crystals to yield fully reliable ΔV data. It was determined that a sample should contain at least 50 crystals if velocity bias resulting from group clustering of c axes in coarse-grained ice is to be avoided. A small but significant decline in Vp↓ with aging of the ice cores, as deduced from ultrasonic measurements made in the liquid-filled drill hole, is attributed to the presence of oriented intracrystalline cracks that form in the cores as they relax from the environmental stresses. A similar series of P wave velocity measurements performed on cores from the 258-m-thick Ross Ice Shelf at Little America V also yielded data in good agreement with the observed c axis fabrics. However, these particular cores are characterized by two distinctive fabrics that both exhibit a circular distribution of c axes about a vertical symmetry axis but which cannot generally be distinguished from one another solely on the basis of ΔV values. To resolve ambiguities of this kind, the ultrasonic measurements must be supplemented by periodic inspectins of fabrics in thin sections. As a general rule, thin section checks of c axis orientations and ice textures should always be made in conjunction with ultrasonic velocity measurements not only to verify the exact nature of the fabrics but also to determine any inclination of the fabric symmetry axis with respect to the direction of P wave transmission. Subject only to these precautions, the ultrasonic technique has proven to be a fast and powerful tool for determining both the nature and extent of crystal anisotropy in ice sheets. Studies of cores from Byrd Station and Little America V together with fabric data from several other locations in East Antarctica, suggest that crystal orientations within the Antarctic Ice Sheet tend to be characterized by either single- or multiple-pole clustering of c axes about a vertical symmetry axis.