The macroscopic anisotropies, which are caused primarily by crystallographic textures, have significant effects on the formability of metal sheets and were extensively investigated experimentally and theoretically. Among the numerous theoretical investigations, the phenomenological approach is based on the classical theory of plasticity, in which the plastic behavior of metals is assumed to be well described by analytical functions proposed by Hill, Hosford and Barlat etc.. Because of its simplicity, the phenomenological approach is widely used in finite element method for plastic forming analysis, but this method lacks direct connection between textures and the revealed anisotropies. An alternative is the Taylor--Bishop--Hill (TBH) model which adopts the crystal plastic theory and explicitly takes the crystallographic textures into account, and thus can be used to analyze the anisotropic phenomena on a physical basis. However, implementation of the TBH model into the analysis of industrial forming process is a real tedious task, needing large amount of computational skill and computer resources. Besides, the TBH polycrystalline model does not satisfy the stress equilibrium condition between grains. The viscoplastic self--consistent (VPSC) model for polycrystalline is also a crystal plastic scheme, but it satisfies both strain compatibility and stress equilibrium conditions. In this study, mathematical models for the Lankford coefficient (r value), uniaxial tensile yield stress and yield locus were established based on the polycrystalline VPSC scheme. The effects of ideal crystallographic textures on the macroscopic anisotropy of fcc materials were analyzed. The results show that the minimum r values of Cube and Goss textures appear at an angle of about 45° from the rolling direction (RD), the r values of Cube at 0° and 90° are both approximately equal to unity whereas the r value of Goss at 90° is much higher than that of 0°. For the Cu, Bs and S textures, their maximum r values appear at the angle of about 45° from RD, and their r values of 0° and 90° present some asymmetries. The uniaxial tensile yield stresses of these ideal textures exhibit corresponding characteristics to their r values and the shape of yield locus also varies accordingly. The simulation results are in agreement qualitatively with those of TBH model and phenomenological theory.