The mechanical properties of the perivascular interstitium surrounding large pulmonary blood vessels are defined in terms of interstitial fluid pressure, interstitial compliance, and interstitial hydraulic resistance. Interstitial pressure is one of the main forces which determine liquid filtration across the microvascular barrier. Interstitial compliance is a measure of the ability of the interstitium to swell with hydration which increases interstitial pressure and reduces the filtration rate. Interstitial pressure and compliance are functions of the elastic properties of the surrounding lung parenchyma and the vessel wall. Solid continuum mechanics are used to describe the behavior of the lung parenchyma. The transport properties of the interstitium are described in terms of a porous material whose fluid resistance is determined by a permeability constant. The dynamics of interstitial fluid are governed by the coupling of the flow with the elastic environment. An electrical analog model is developed to predict the growth of interstitial fluid cuffs during edema formation.