We have developed a model of forces developed in lung tissue in which the stress-bearing units are heterogeneous. Each element of the fiber network is composed of an idealized elastin and collagen element in parallel. Elastin is represented by linear springs and collagen by stiff strings that extend without resistance until taut. The model can quantitatively account for the nonlinear shape of the length-tension curve of lung tissue strips when the knee lengths of the collagen fibers are distributed according to an inverse power law. The novel feature of this model is that as macroscopic strain increases the load is carried by progressively fewer elements with progressively higher forces, and preferential pathways of force transmission emerge within the matrix. The topology of these self-organizing pathways of force transmission takes the rough appearance of cracks, but, unlike real cracks, they represent the locus of force concentration rather than force release.