The lean premixed combustion allows for reducing the production of thermal NOx, therefore it is largely used in industrial combustion. Lean premixed combustors are, however, prone to combustion instabilities. An analytical model was developed by Büchner [14] in order to predict the stability limits of combustion systems. A significant input of this model is the damping ratio, which should be determined from experiment or numerical simulation. In the present work a numerical investigation of the pulsating, non-reacting flow in a model combustion chamber and a coupled system of burner plenum and combustion chamber is presented. The results of the Large Eddy Simulations (LES) are compared with the analytical model and experimental data. The prediction of the damping ratio by LES is very good. It depends, however, on special boundary conditions. By means of the simulations the basic assumptions made by the analytical model could be confirmed. The pulsating flow in the region of the exhaust gas pipe was analyzed and compared with the literature. The major damping mechanisms were identified in the system and a source of combustion instabilities could be localized.