Due to the high temperature of the flue gas flowing at high velocity and pressure, the wall cooling is extremely important for the liner of a gas turbine engine combustor. The liner material is heat-resistant steel with relatively low heat conductivity. To accommodate outside wall forced air cooling, the liner is designed to be thin, which unfortunately facilitates the possibility of high-amplitude wall vibrations (and failure due to fatigue) in case of pressure fluctuations in the combustor. The latter may occur due to a possible occurrence of a feedback loop between the aerodynamics, the combustion, the acoustics, and the structural vibrations. The structural vibrations act as a source of acoustic emitting the acoustic waves to the confined fluid. This leads to amplification in the acoustic filed and hence the magnitude of instability in the system. The aim of this paper is to explore the mechanism of fluid–structure interaction (FSI) on the LIMOUSINE setup which leads to limit cycle of pressure oscillations (LCO). Computational fluid dynamics (CFD) analysis using a RANS approach is performed to obtain the thermal and mechanical loading of the combustor liner, and finite element model (FEM) renders the temperature, stress distribution, and deformation in the liner. Results are compared to other numerical approaches like zero-way interaction and conjugated heat transfer model (CHT). To recognize the advantage/disadvantage of each method, validation is made with the available measured data for the pressure and vibration signals, showing that the thermoacoustic instabilities are well predicted using the CHT and two-way coupled approaches, while the zero-way interaction model prediction gives the largest discrepancy from experimental results.