Filamentary networks play an important role both in engineering (fiber reinforced materials) and in biology (cytoskeleton or porous bone material). When investigating the elastic properties of such materials, an often used model consists of a random network of deformable filaments attached to each other by cross-links. Most often, these cross-links form hinges, sometimes they are rigid connections. The investigations revealed that either bending or stretching dominated regimes govern the behaviour, depending on the density of the network or on the bending or stretching stiffness of the rods. We plan to further investigate and extend this model by including moment bearing hinges at the cross-links. We expect that in the extended model the shear strains will play important role. We also intend to shed light on the role of heterogeneity in such models, that is, what happens when the size or mechanical properties of the rods are different. We also investigate the gradual break down of such networks under inceased imposed strain. The experience obtained from the model is expected to be useful in the investigation of the cytoskeleton and fiber reinforced materials.