This paper reports on Large Eddy Simulation (LES) of turbulent premixed methane/air flames approaching blow-off. The study focuses on a stable flame, and on a flame just prior to blow-off, both stabilized by the Cambridge bluff-body burner. For turbulence-chemistry interaction, a model based on transported probability density function (TPDF) in conjunction with Eulerian stochastic fields is used. Velocity, species-concentration and heat release fields were first compared against experimental data showing good agreement. The results demonstrate that simulations of such complex combustion phenomena are possible and that the model is capable of reproducing the flame and the flow characteristics under both stable and close to blow-off conditions. A blow-off sequence was then examined and the results were used to evaluate some of the theories and mechanisms responsible for flame blow-off. It was found that the local extinction in the shear-layers had only minor impact on the flame blowing off and that the blow-off is a result of a series of events starting with the flame migrating into the recirculation zone. In the end, a mechanistic explanation is proposed for this series of events leading to full extinction of the flame. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.