Stress profiles develop in a porous material due to a gas-phase pressure difference and subsequent gas flow. If stresses become tensile, material failure (explosion and blistering) can occur. Stress profiles are calculated for an asymmetric inorganic porous disk-like membrane material placed in a pressure vessel, which is depressurized. The stress that develops in the membrane material depends on the gas-phase pressure and the porosity. The gas-phase pressure is a function of place, time and characteristics of the membrane, the vessel and the valve. Two regimes are identified for membrane depressurization, and a critical initial pressure is defined below which tensile stresses cannot develop. The theory presented combines the dusty gas model with balances for mass, momentum, and mechanical energy.