Abstract: Based on the uniaxial tensile test of round-bar specimens of isotropic homogeneous elasto-plastic material, the correlation between the deformation characteristics and the stress-strain constitutive relationship are analyzed theoretically. By the finite element method, the necessary conditions for the formation of necking and the formation process of the actual necking morphology are discussed. The results show that the material stress-strain constitutive properties and the specimen are non-ideal, and that a cylinder is a necessary condition for necking. When the equivalent plastic strain (ε_p) reaches a certain critical value, the flow stress (σ₀) no longer increases with the increase of ε_p. The internal fractures formed in the later stage of necking are the reasons for the smaller curvature radius of the arc contour at the minimum cross-sectional position of the necking area.