This article describes the numerical framework for a reduced order tool which aims at simulating combustion instabilities in liquid rocket engines. The numerical framework relies on the projection of the pressure fluctuations on the eigenmodes of the system. Pressure fluctuations are solutions of the wave equation of the system. After projection on the eigenmodes, the wave equation takes the form of series of second order harmonic equations with source terms that drive combustion instabilities and damping terms that attenuate them. A test rig was developed to study cavity interactions, injector impedance as well as damping effects. Damping rates measured on the test rig show a trend which is consistent with what is observed in liquid rocket engines. On a whole, the test rig can be used to validate simplified models of combustion instabilities. The global framework of the reduced order tool developed to predict combustion instabilities in liquid rocket engines was first validated by comparing the data from simulations against experimental results from the test rig in a series of non-reacting experiments. The tool was then used in a case study of a full-scale rocket engine. This engine, under certain operating conditions, exhibits instabilities. Stable and unstable behaviors have been revealed by the temporal evolution of pressure amplitudes. Nomenclature p = pressure [Pa] x = position vector [m,m,m] t = time [s] * PhD, Ingénieur ISAE-ENSMA, m.