An isotropic constitutive model for the parenchyma of lung has been derived from the theory of hypo-elasticity. The intent is to use it to represent the mechanical response of this soft tissue in sophisticated, computational, fluid-dynamic models of the lung. This demands that the continuum model be accurate, yet simple and efficient. An objective algorithm for its numeric integration is provided. The response of the model is determined for several boundary-value problems whose experiments are used for material characterization. The £ First annual report to Pacific Northwest National Laboratory from Saginaw Valley State University reporting on progress made under grant number 136492. The project described was supported by Award Number R01HL073598 from the National Heart, Lung, and Blood Institute to Pacific Northwest National Laboratory. The content is solely the responsibility of the author and does not necessarily reflect the official views of the National Heart, Lung, and Blood Institute or the National Institutes of Health.2 effective elastic, bulk, and shear moduli, and Poisson's ratio, as tangent functions, are also derived. The model is characterized against published experimental data for lung.A bridge between this continuum model and a dodecahedral model of alveolar geometry is investigated, with preliminary findings being reported.