© 2017 Elsevier Ltd A multiscale, physically-based, reaction-diffusion kinetics model is developed for non-steady-state transport of simple gases through a rubbery polymer. Experimental data from the literature, new measurements of non-steady-state permeation and a molecular dynamics simulation of a gas-polymer sticking probability for a typical system are used to construct and validate the model framework. Using no adjustable parameters, the model successfully reproduces time-dependent experimental data for two distinct systems: (1) O2quenching of a phosphorescent dye embedded in poly(n-butyl(amino) thionylphosphazene), and (2) O2, N2, CH4and CO2transport through poly(dimethyl siloxane). The calculations show that in the pre-steady-state regime, permeation is only correctly described if the sorbed gas concentration in the polymer is dynamically determined by the rise in pressure. The framework is used to predict selectivity targets for two applications involving rubbery membranes: CO2capture from air and blocking of methane cross-over in an aged solar fuels device.