Abstract: One of the biggest challenges for soft materials is to establish statistical mechanical models to correctly describe the relationship between its microstructure and macroscopic mechanical properties, and the statistical models for rubber-like materials still have some imperfections. Based on the macroscopically isotropic, continuous uniform and incompressible properties of rubber-like materials, combined with a non-Gaussian statistical model for molecular chains, a new elastic model for rubber material is proposed. The force transfer path between the corresponding points on the representative volume element is described by a subnetwork constrained to a region as a spiral helical tube, whose surfaces all deform affinely with the macroscopic deformation. The sub-network consists of molecular chains or chain segments linked end-to-end with random orientation and length. Hence, the constitutive model describing the macroscopic mechanical characteristics of the material is derived from the entropy of the subnetwork. A large number of test data were used to fit the constitutive model, which show that the model has very good accuracy. Especially, the proposed model with two parameters show very high reliability that it gives good predictions of the three basic test with the parameters derived from data-fitting with uniaxial tension data only. With the proposed curved affine tube confinement, this model can explain the incompressible properties of the material from the microstructure scale, overcome the shortcoming of straight tube model, and build a new model for the correlation between the stochastic at the micro scale and the uniform at the macro scale.