We construct constitutive relations for metals subjected to large plastic strains at high temperatures. A metal is an elastoviscoplastic medium strengthening under plastic strains and softening owing to return processes and dynamic recrystallization [1, 2]. In [3–7], constitutive relations were obtained for a viscoplastic medium under high-temperature plastic strains. These relations include kinetic equations describing the return process [4], recrystallization [5, 7], and the joint action of the return process and recrystallization [3, 6]. In [3, 7], the recrystallization nucleus density is additionally introduced, and in [3, 6], the increase in metal recrystallization volumes is taken into account. In the mathematical model in [5], the authors explicitly use separate points of the strengthening curves, which narrows the scope of the model. An analysis shows that, to obtain an adequate description of metal rheology under complicated laws and for a wide range of the strain rate variation, it is necessary to improve the constitutive relations obtained earlier.