The insensitive explosive PBX 9502 contains 95wt-% of TATB crystals and a plastic bonding agent (Kel-F). The TATB crystals have plate-like morphology, similar to that of graphite or boron nitride. We have used X-ray diffraction to measure the preferred orientation (texture) of the TATB crystals in parts fabricated by pressing PBX 9502 powder. Independently, we have used finite-element calculations to derive the direction and magnitude of the shear imposed during the consolidation of this composite material. Based on our results, we propose that the texture develops because the applied shear causes the TATB crystals to rotate such that their (002) basal planes are parallel to shear planes. The texture predicted by this model agrees qualitatively with that measured at various locations within the PBX 9502 compact. Further validation of this model is obtained by the measurement of the thermal expansion coefficient of PBX 9502, which is highly anisotropic.