We present a reformulation of the finite strain, rate dependent inelastic glass–rubber material model suggested by Buckley and Jones (1995) and extended by Adams et al. (2000) for modeling the deformation of amorphous polymers in the Lagrangian logarithmic strain space. This not only warrants a hyperelastic characterization in the bonding part which remedies problems associated with hypoelastic approaches devising objective stress rates selected on ad hoc basis, see, e.g., Dooling et al. (2001) and Li and Buckley (2009), but also allows a transparent and naturally objective implementation analogous to the geometrically linear theory. A numerical implementation into ABAQUS is pursued where algorithms for stress update and tangent moduli computations are reported. It is shown that significant reduction in nonlinear equation system size is possible in the computation of both bonding and conformational part. The characterization tests include constant-width tension, equi-biaxial tension, and simple shear. To demonstrate the robustness of the developed framework, two hypothetical problems of extreme deformation under tensile and combined tensile and torsion loading are considered. Finally, simulation of an injection stretch-blow molding process is presented as an application problem.