Deuterium nuclear magnetic resonance experiments on rubber networks under uniaxial stress display a characteristic feature : A doublet structure for network chains and for free chains diffusing in the network. The doublet structure can be explained in a mean field theory by introducing orientational segmental interactions in the network system. A mean field theory of this kind is explicitly developed for a network system on a cubic lattice. Monte Carlo simulations on a cubic lattice are performed and compared to theory. Segmental interactions are simply introduced by applying the concept of mutually and self-avoiding chains in the simulation. It is confirmed that the segmental interactions introduce a uniaxial segmental orientation in the sense that each segment shows an orientational behavior as being under the influence of a uniaxial external field. The mean field theory is shown to be well reproduced by the simulations. The calculation of the nuclear magnetic resonance spectrum for the model network of the simulation gives a doublet structure only for the case where steric interactions are present.