Abstract: Based on experimental results, uniaxial and nonproportionally multiaxial ratcheting of cyclically stable materials is described constitutively at room temperature. A new visco-plastic constitutive model feasible for engineering application is established in the framework of unified visco-plasticity. The determination of material parameters used in the model is elaborated in detail, and the values of material parameters for U71Mn rail steel are obtained directly from the experimental inelastic uniaxial tensile stress strain data. The capability of the proposed constitutive model is verified by simulating the corresponding experiments of U71Mn rail steel at room temperature. It is shown that the simulated results are in good agreement with the experimental ones.