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We present here an experimental study of the influence of the aeroelastic coupling between the combustion chamber walls and the acoustic fluid field on the onset and development of thermoacoustic instabilities in stoichiometric propane-air premixed flames. A horizontal quasi-two-dimensional Hele–Shaw chamber formed by two parallel plates separated a small distance h is used. The flames are ignited at the open end, in contact with the atmosphere, and propagate towards the opposite closed end. The experiments reveal three distinct propagation regimes determined by the stiffness of the plates and the evolution of the pressure perturbation generated during ignition: (i) for sufficiently rigid plates, we observed secondary acoustic instabilities with large amplitude oscillations in the direction of propagation of the flame; for flexible enough walls to be compliant with ignition-related pressure changes, (ii) the propagation of the flame undergoes small-amplitude oscillations (primary acoustic instabilities) along the channel or (iii) it is smooth with no oscillations whatsoever. The flexural rigidity of the plate is modified experimentally by changing both the width W and thickness h w of the top plate of the Hele–Shaw cell. The data recorded by the pressure transducer and the accelerometer is used to plot a stability map in the W − h w parametric space to define the combination of structural parameters that triggers the onset of thermoacoustic instabilities. Our experimental measurements, supplemented with results from a theoretical analysis of the walls vibration modes, indicated that deformation-induced volume changes of around 0.1% of the volume of the Hele–Shaw cell are sufficient to suppress thermoacoustic instabilities. [ABSTRACT FROM AUTHOR]