Ramjet burners are known to produce highly unsteady operating conditions with strong couplings between combustion, acoustics and flow dynamics. Predicting such operating limit-cycles still remains a difficult task for Computational Fluid Dynamics (CFD) although recent use of Large Eddy Simulation (LES) clearly opens new possibilities. The main difficulties for LES are to properly address numerically specific flow features at the same time. For example, a proper representation of the acoustic ramjet eigenmodes necessitates for the solver to be able to treat shocks often present at the inflow conditions without interfering with the low Mach number flow in the region of combustion. Chemistry modelling is another difficulty and it is still not clear what level of description is sufficient to reproduce the unsteady coupling between heat release and acoustics. Turbulent combustion modelling is an additional problem. Finally, such confined burners are strongly influenced by heat losses and although such issues are rarely addressed numerically, the burner stability is expected to be strongly dependent on its thermal equilibrium. Despite these difficulties and as discussed in this work, LES can greatly contribute in the understanding of the key mechanisms at play in the expression of the ramjet oscillatory operation. Prior to this demonstration, key elements needed for such LES are detailed: shock capturing techniques and chemical modelling. The effect of the chemistry model on the LES results is briefly discussed. The proposed strategy is then confronted to three operating conditions of an experimentally measured ramjet burner. Although the scheme is quite simple and essentially relies on the dynamical response of combustion, i.e. competition between the local flow and flame speeds, most of the mean flow features are well reproduced for the three operating L. Y. M. Gicquel (B) CERFACS, Flow Turbulence Combust (2011) 87:449-472 conditions. Peak pressure spectra are well predicted indicating the proper relative energy content distribution of the unsteady LES predictions.