The constitutive relationships of a 35Mn2 steel during hot compression testing were systematically investigated using three methods. The first method is a conventional hyperbolic sine equation with peak stress dependent constants, the activation energy Q determined by this method is about 278 kJ/mol, very close to the austenite lattice self--diffusion activation energy (270 kJ/mol), indicating the rate-controlling mechanism is dislocation climb controlled by diffusion. The second method is a developed hyperbolic sine equation with strain dependent constants, comparing with experimental results, the correlation coefficient and average relative error ofpredicted and measured values are 0.991 and 4.19%, respectively, indicating that the developed equations can give an accurate estimate of the flow stress for the experimental steel. The third method is a physically based approach accounting for the dependence of the Young’s modulus and the self-diffusion coefficient of austenite on temperature, which is also capable of representing the flow stress of the material as a function of the deformation conditions, but the fitting precision by this method is lower than by the conventional hyperbolic sine equation, and through modification, the fitting precision of the physically based approach is improved in this work.