AbstractThis work presents a new extended Chaboche’s viscoplastic law at finite strains, so that the classical Chaboche’s theories can be applied to the physical and numerical simulation of metals processing and behavior description of spatial metal structures. The extension is based on a new dissipation inequality at finite strains. The evolution equations are formulated in terms of the corotational rates of the elastic logarithmic strain and the strain-like internal variable conjugate to the back stress as well as the material time derivative of the accumulated plastic strain. The stress equation is expressed on the basis of the hyperelastic theory. Therefore, the possible inconsistency with elasticity, caused by the hypoelastic equations, is completely removed. A set of numerical examples with finite deformations are presented to prove the effectivities of the new model and numerical algorithms.