Background <p>Accurate prediction of the plastic behavior of AA2024‒T4 requires a deep understanding of the mechanical response of the material under different loading conditions. For alloy sheets, the material orientation and deformation are two important factors whose effects should be clarified.</p> Objective <p>This work focuses on the complex relationships among the material orientation, deformation, and tension‒compression asymmetry of AA2024‒T4.</p> Methods <p>The tension, compression, and shear responses of materials at different orientations are experimentally investigated through dog bone, cuboid, and butterfly specimen, respectively. In addition, the tension‒compression asymmetry is embedded in the anisotropic parameters rather than an additional independent parameter.</p> Results <p>Tension‒compression asymmetry is sensitive to orientation and degree of deformation. The tension‒compression asymmetry tends to be stable with increasing degree of deformation. But the evolution law of tension–compression asymmetry can be affected by orientation.</p> Conclusions <p>An additional parameter describing the asymmetry is required for isotropic plastic modeling. This parameter can be ignored when the anisotropic situation is considered because such an effect will be implied in the anisotropic parameters. In addition, the influence of degree of deformation on tension–compression asymmetry and plastic anisotropy can be reflected by the evolutions of anisotropic parameters.</p>