The increase in the strength of the Al–Cu–Mg alloys is to a large extent due to the formation and distribution of submicroscopic θ-Al2Cu and S-Al2CuMg phases in the aluminum (α-Al) matrix, which causes these alloys to have unique properties such as high initial hardening rate. This paper aimed to examine the anisotropic plasticity and flow behavior of the AA2024-T3 aluminum alloy by measuring the distinctive properties of each of the θ-Al2Cu, S-Al2CuMg, and α-Al phases at the micro-level and using a microstructure-based crystal plasticity model during single-strand tensile strength. The real microstructure of AA2024-T3 aluminum alloy obtained from scanning electron microscopy (SEM) was utilized in the calculations using the polycrystalline image processing method of the phases as a Representative Volume Element (RVE). Each phase’s crystal orientations and texture were randomly generated, given the lattice parameters and their crystal structure. The computational results were compared with the experimental data of the AA2024-T3 aluminum alloy tensile test, the data of the crystal plasticity model without considering the microstructure, and the Johnson-Cook model. Given the heterogeneity of the microstructure and crystal orientations of the grains, it was shown that the maximum internal stress under tensile loading occurred along with local hardening in the α-Al phase adjacent to the grains of the θ-Al2Cu and S-Al2CuMg phases, which was about 43300 MPa.