Monte Carlo simulations of dense polymer networks under uniaxial strain were carried out using the three-dimensional bond fluctuation model. Particular attention is paid to the distribution of orientation for individual chain segments within the network and to comparison with experimental results from deuterium nuclear magnetic resonance (D-NMR). The simulated D-NMR spectrum has a split double-peak structure indicating that the segments have a degree of uniaxial orientation about the strain axis. The splitting disappears if the excluded volume restriction is removed from the simulation. This confirms that excluded volume and chain packing are important in determining orientational behavior. D-NMR spectra for dangling chain ends and for free chains within a network are also simulated and compared with experimental results. When the model dynamics is modified so that chains may pass through each other but the excluded volume restriction is maintained, it is found that the D-NMR spectrum is almost unchanged from the usual network. Thus, topological entanglements appear to have very little effect on the orientational behavior, at least for the relatively short chain lengths that we simulate here. The autocorrelation function for the uniaxial order parameter, [P-2(cos theta)], for each bond can be well-fitted by a stretched-exponential relaxation function. Relaxation times are almost constant along the majority of the chain but are significantly shorter within a few segments of free chain ends and significantly longer within a few segments of fixed chain ends. The apparent shapes of the D-NMR spectra are influenced by the total duration of the simulation, even when the simulation is several orders of magnitude longer than the orientational relaxation time of the chain segments. This observation is explained theoretically. Both experimental and simulated spectra have broad "wings" in addition to the central split peak. It is found that the spectrum for the chain middles and chain ends are very similar; i.e., segments close to chain ends do not contribute preferentially to the wings of the spectrum. It is found that chains with short end-to-end distances contribute principally to the central doublet of the full network spectrum. Segmental orientation in these chains is strongly influenced by excluded volume and chain packing and is insensitive to the end-to-end vector. Chains with long end-to-end distances contribute almost entirely to the wings of the full network spectrum, and segmental orientation is influenced principally by the chain end-to-end vector.