Abstract: As the strain accumulation of metal material reaches a certain critical value in plastic deformation, the induced dynamic recrystallization (DRX) may decrease the flow stress, and the critical condition of metal material and its dynamics are closely related to the deformation conditions. Based on the hot compression test data of 45 steel deformed at a temperature range of 450-850℃ and strain rate of 0.1-30 s^-1, the relationship between critical strain of DRX (ε_c) and deformation parameters Z was analyzed by Poliak-Jonas method. Taking ε_c as the critical point of stress-strain curves, a constitutive model for 45 steel at two stages, whether or not dynamic recrystallization occurred, was presented based on the E-M equation and dynamic recrystallization theory. The results show that predicted values of the constitutive model are in good agreement with those of measurements.