Uniaxial stress-strain properties of highly swollen and stretched rubbers are discussed in the framework of a recently developed non-Gaussian network model that considers the finite extensibility of network chains together with topological chain constraints. The finite extensibility is described by the well-known inverse Langevin function of the network chain end-to-end distance. The model consequently distinguishes between topological constraints coming from packing effects of neighboring chains and from trapped entanglements. Whereas the latter act as additional network junctions, the packing effects are modeled in a mean-field-like manner through strain-dependent conformational tubes. The calculated Gaussian contribution to the total modulus, the swelling dependence of the infinite strain modulus, and the tube constraint modulus of natural rubber (NR) samples are determined. It is found that the infinite strain modulus varies linearly with the polymer volume fraction phi, whereas the tube constraint modulus varies as phi(4/3). Both observations agree with the predictions of the presented model. Contrary to literature data that were estimated from stress-strain experiments on swollen networks in the framework of Gaussian statistics, the tube constraint modulus (which is proportional to the C-2 value of the Mooney-Rivlin equation) is found to vanish in the limit phi --> 0, and not at a finite universal value phi approximate to 0.2.