In the present work, results of attempts to capture the high-frequency combustion instability in a rocket combustor equipped with hydrogen (H 2 ) / oxygen (O 2 ) injector are shown. To enhance the coupling between heat release rate fluctuations and pressure oscillations, the injector element is installed at the off-center of the combustion chamber in the simulation. Two-dimensional simulations are conducted for a single-element combustor. The flow forcing by modulating the mass flow rate of O 2 injection is attempted to excite the first transverse (1T) mode of chamber. The simulation results indicate that the amplitude of 1T mode is increased by the flow forcing. To clarify a driving mechanism for the growth of pressure oscillations, the simulation results are analyzed using the Rayleigh index. Simulations are then extended to three-dimensional LES for a combustor equipped with five shear-coaxial injector elements. The obtained results of pressure field and the Rayleigh index are compared with those of a single element combustor. The effects of multiple flames on the pressure field are examined. Nomenclature c = Speed of sound D = Width or diameter E = Total energy per unit mass f = Frequency m = Mass flow rate p = Pressure q = Heat flux q = Heat release rate T = Temperature t = Time u = Velocity V = Diffusion velocity or volume x = Cartesian coordinate Y = Mass fraction of species Subscripts i, j = Cartesian direction k = Species k property 0 f = Time average Superscripts f = Filtered quantity f = Resolved quantity f = Fluctuation sgs = Sub-grid scales 1 2 Symbols = Specific heat ratio = Density = Stress tensor = Production rate