Abstract: In the present study, the quasi-static tensile behavior of the smooth round bar specimens was comprehensively investigated, prompted by the recognized limitations of existing theoretical frameworks in accurately representing complex deformation phenomena, including local stress non-uniformity and the development of necking in metallic materials. The accuracy of the numerical model is validated through comparative analysis of simulated and experimentally obtained results in terms of load-displacement curves and cup-cone fracture morphologies. By examining the evolution of Mises stress, damage variables, cross-sectional damage distribution, and stress triaxiality, the stress transformation mechanisms during necking are elucidated. Furthermore, the Bridgman effect governing post-necking stress states is theoretically analyzed, establishing the relationship between axial stress and equivalent stress in the necked region. Finally, the applicability and accuracy of commonly used methods for obtaining the true stress–strain relationship are critically evaluated, thereby deepening the understanding of the material’s stress–strain behavior, stress states, and deformation.