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An improved pressure-based method has been applied to predict the two-dimensional instability analysis of liquid-fuelled rocket engines. This method is non-iterative for transient flow calculations and applicable to all-sped flows. Validation cases include the shock-tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.KEY WORDS Pressure-based method All-speed Blast wave Two-phase flow Combustion instability

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