<p>This paper presents a time integration algorithm for hyperelasto-viscoplasticity, formulated in the intermediate configuration&#xa0;and employing a tensor exponential function to ensure plastic incompressibility. For kinematic hardening, an additional intermediate configuration is introduced, following the multiplicative decomposition of the plastic deformation gradient, as established in the viscoplasticity literature. The proposed time integration scheme employs a system of four simultaneous equations to solve for fourteen unknowns, including both tensor- and scalar-valued variables. To reduce computational complexity, symmetric tensor valued variables are employed, thereby&#xa0;minimizing the number of unknowns. Additionally, a consistent tangent modulus tensor based on the intermediate configuration is derived. The efficiency of the framework is then demonstrated through two case studies: simple shear deformation and a finite element analysis. Material responses for the simple shear deformation, considering no hardening, isotropic hardening only, kinematic hardening only, and mixed hardening, are validated by comparison with results from the literature, demonstrating excellent agreement. Under all specified conditions, the modeling of the Bauschinger effect region aligns perfectly with the available results. Even under very large applied shear deformations (up to 10), no shear-stress oscillations are observed when only kinematic hardening is considered. In the finite element case studies, a cantilever beam under large rotation and bending forming processes is analyzed, with results highlighting the robustness and accuracy of the proposed numerical implementation.</p>