A new molecular constitutive model for rubber-like elasticity has been developed based on the same theory structure and terminology as Doi-Edwards type constitutive models for topologically entangled polymeric fluids. The new model using the independent alignment approximation (IAA) successfully predicts the effective modulus (Mooney ratio) in uniaxial extension and compression with accuracy nearly equal to the nonaffine slip tube model of Rubinstein and Panyukov. However, unlike the nonaffine slip tube model of Rubinstein and Panyukov, our Doi-Edwards IAA rubber model can be simply extended to arbitrary deformation types as well as make theoretical predictions for the fourth moment of the segmental orientation distribution function in general uniaxial deformations which is relevant to polarized Raman scattering experiments. We demonstrate this capability explicitly. The new Doi-Edwards rubber model demonstrates that there are apparently other, simpler, essentially ad hoc means to address the effects and character of the trapped topological entanglements in elastomers at moderate and high strains than the much more complex nonaffine slip tube model.