Geometrical and different physical nonlinearities have to be taken into account in order to model elastomeric material. In the present contribution, a novel approach of rubber elasticity is introduced. The approach considers the topological constraints as well as the limited extensibility of network chains in filled rubber. Subsequently, a formulation of finite viscoelastic damage is derived. With this description at hand, softening effects as well as time and frequency dependency of the material can be characterized. The goal of the present paper is twofold. Firstly, the constitutive formulations are introduced. Moreover, computational aspects are stressed. The shown approaches are presented in a format ready for a finite element implementation.