A model of a nonlinearly elastic polymer network is proposed, which allows the inhomogeneity and complex topological character of the network structure to be described in an explicit form. The deformation and strength behavior of the network was studied depending on the structure inhomogeneity. It was shown that the introduction of geometric disordering (pertaining to the arrangement of junctions) and stiffness inhomogeneity (the scatter of the polymer chain contour lengths and, therefore, the stiffness of chains) can provide for not more than a four-to fivefold decrease in the strength as compared to regular homogeneous structures.