Traditionally, simple flow stress laws including Hollomon and Swift models have been much employed. However, the simple models or laws could cover only limited part of materials including cold forgeable steels because they could be appropriately described by the models. Nowadays, special metals and new materials are being widely employed and new material models are needed for their accurate description of flow stress. In this paper, flow stress models of metallic materials at room temperature are reviewed and the tensile test is recovered with an emphasis on the post-necking strain hardening of material models. The necking point, consuming two degrees of freedom, is emphasized in characterizing the material constants because plastic deformation after it is very sensitive to itself. The well-known material models are first grouped into three categories such as Ludwik involving Hollomon, Voce, and Swift flow stress models. These three fundamental flow stress models are investigated in terms of tensile test to reveal their post-necking strain hardening behaviors using purposely the rigid-plastic finite element method, which predicts the necking point exactly in the engineering sense without any imperfection of cylindrical specimen.
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