The paper focuses on developing and justification of the flame extinction model for large eddy simulations of under-resolved turbulent diffusion flames. The model is based on the perfectly stirred reactor (PSR) concept, in which the residence time is coupled with the local strain rate, and the radiative losses from the reaction zone are taken into account. The single-step global reaction of fuel oxidation is considered. A possible way to calibrate the kinetic parameters is that by fitting measured values of flame temperature and strain rate at diffusive extinction (blow-off). By comparing the simulation results with experimental data available for methane-air and heptane-air flames and with the published predictions made by the activation energy asymptotics for the ethylene-air flame, it is demonstrated that the PSR model is capable of evaluating flammability bounds of the diffusion flame, including high-strain blow-off and low-strain quenching (i.e., diffusive and radiative extinction). The confluence of these bounds is shown to produce the minimum extinguishing concentration of an inert diluent. For the flames diluted by nitrogen, carbon dioxide, water vapor, or argon, the minimum extinguishing concentrations predicted in this way by the non-adiabatic PSR model are shown to agree with the measured values. Possibility of formulating a unified extinction criterion, the Damkohler number, is confirmed. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.