We propose a modeling framework for finite viscoelasticity, inspired by the kinematic assumption made by Green and Naghdi in plasticity. It differs from the widely used multiplicative decomposition of the deformation gradient in that the intermediate configuration becomes unnecessary. With the advent of generalized strains, the adopted kinematic setting allows a flexible mechanism in separating inelastic deformation from the total deformation. For quadratic configurational free energy, the framework yields a suite of finite linear viscoelasticity models governed by linear evolution equations. We show that the framework recovers established models, including those by Green and Tobolsky (1946), Miehe and Keck (2000), and Simo (1987), when the Seth-Hill strain is used with the strain parameter being−2, 0, and 2, respectively. Moreover, the model is extended by adopting coercive strains, which facilitate modeling the non-equilibrium branch using micromechanical models. Building upon this framework, we further consider the non-Newtonian effect and material anisotropy. The viscous behavior is characterized through a non-negative, convex dissipation potential. It directly results in the evolution equations for the internal variables by satisfying the maximum entropy production principle, and its design allows for systematic incorporation of the non-Newtonian models. In the meantime, anisotropy is conveniently addressed within the framework, since it circumvents the debated and troubling issue of accounting for the evolution of the symmetry groups on the intermediate configuration. We leverage the techniques based on the structure tensors and pseudo-invariants to introduce anisotropy into both the free energy and the dissipation potential. The capability of the models is examined by employing a suite of experimental data for viscoelastomers, demonstrating their effectiveness and potential advantages in the fitting and prediction of the mechanical behaviors of real materials. The finite element implementation and a robust structure-preserving time integration of the models are also discussed. The results demonstrate that a unified and versatile approach to modeling viscoelasticity is established, and it offers new insights into both theoretical foundations and practical applications.