Summary: Internal dissipation always occurs in irreversible inelastic deformation processes of materials. The internal dissipation inequalities (specific mathematical forms of the second law of thermodynamics) determine the evolution direction of inelastic processes. Based on different internal dissipation inequalities several finite strain inelastic constitutive laws have been formulated for instance by J. C. Simo [Comput. Methods Appl. Mech. Eng. 99, No. 1, 61–112 (1992; Zbl 0764.73089)], J. C. Simo and C. Miehe [Comput. Methods Appl. Mech. Eng. 98, No. 1, 41–104 (1992; Zbl 0764.73088)], A. Lion [Acta Mech. 123, No. 1–4, 1–25 (1997; Zbl 0910.73019)] S. Reese and S. Govindjee [Int. J. Solids Struct. 35, No. 26–27, 3455–3482 (1998; Zbl 0918.73028)], R. C. Lin and U. Schomburg [Comput. Methods Appl. Mech. Eng. 192, No. 13–14, 1591–1627 (2003; Zbl 1050.74005)], R. C. Lin and W. Brocks [Int. J. Plast. 20, No. 7, 1281–1311 (2004; Zbl 1066.74521)]. These constitutive laws are consistent with the second law of thermodynamics. As the internal dissipation inequalities are described in different configurations or coordinate systems, the related constitutive laws are also formulated in the corresponding configurations or coordinate systems. Mathematically, these constitutive laws have very different formulations. Now, a question is whether the constitutive laws provide identical constitutive responses for the same inelastic constitutive problems. In the present work, four types of finite strain viscoelastic and endochronically plastic laws as well as three types of \(J_{2}\)-plasticity laws are formulated based on four types of dissipation inequalities. Then, they are numerically compared for several problems of homogeneous or complex finite deformations. It is demonstrated that for the same inelastic constitutive problem the stress responses are identical for deformation processes without rotations. In the simple shear deformation process with large rotation, the presented viscoelastic and endochronically plastic laws also show almost identical stress responses up to a shear strain of about 100%. The three laws of \(J_{2}\)-plasticity also produce the same shear stresses up to a shear strain of 100%, while different normal stresses are generated even at infinitesimal shear strains. The three \(J_{2}\)-plasticity laws are also compared at three complex finite deformation processes: billet upsetting, cylinder necking and channel forming. For the first two deformation processes similar constitutive responses are obtained, whereas for the third deformation process (with large global rotations) significant differences of constitutive responses can be observed.