Rubber-like materials are composed of intensively inter-connected chain-like macromolecules randomly orientated in a network. The chain interactions are established by entanglements or cross-links. Predicting the mechanical response of such materials is still a challenging task which involves comprehensive molecular chain statistics. In the present contribution, a new constitutive model for rubber-like solids is proposed based on reptation theory considering entangled polymers. The model takes into consideration the length of macromolecule between adjacent entanglements as well as a special mechanism of the chain movement. Further features of the model are a non-affine deformation of polymer chains in the network and an approximation of the inverse Langevin function appearing in the non-Gaussian statistical framework. The model includes a few number of physically motivated material constants including the entanglement density and demonstrates good agreement with experimental data.