The formation of rolling texture in the α solid solution and the δ′ phase in various sections of 1424 (Al-Mg-Li-Zn-Sc-Zr) alloy sheets 1.6–8 mm thick is studied using pole and inverse pole figures. The textures of the α solid solution and δ′ phase are shown to be characterized by similar changes in the orientations across the sheets. The medium layer in the sheets has a two-component {011}〈211〉 + {135}〈211〉 texture with the predominant first component. The anisotropy in the mechanical properties of the alloy sheets is characterized by a high yield strength and a low plasticity in the longitudinal and transverse directions as compared to direction at an angle of 45° to the rolling direction. A model for the calculation of the anisotropy in the yield strength of the alloy is proposed; it takes into account the texture in the alloy, the ratio of the volumes of the α solid solution and δ′ phase, and their relative strength.