The mechanical behavior of the lung tissue (expressed by its constitutive equations) has considerable influence on the normal and pathological function of the lung. It determines the stress field in the tissue, thus affecting the impedence and energy consumption during breathing as well as the localization of certain lung diseases. The lung tissue has a complex mechanical response. It arises from the tissue’s structure—a cluster of a very large number of closely packed airsacks (alveoli) and air ducts. Each of the alveoli has a shape of irregular polyhedron. It is bounded by the alveolar wall membrane. In the present study, a stochastic approach to the tissue’s structure will be employed. The density distribution function of the membrane’s orientation in space is considered as the predominant structural parameter. Based on this model the present theory relates the behavior of both the alveolar membrane and that of its liquid interface to the tissue’s general constitutive properties. The resulting equations allow for anisotropic and visco-elastic effects. A protocol for material characterization along the present model is proposed as well. The methodology of the present theory is quite general and can be similarly used with other structural models of the lung tissue (e.g., models in which the effect of the alveolar ducts is included).