A temporal linear stability analysis was performed for a viscous annular liquid sheet exposed to compressible gas flows. An analytical dispersion relation illustrating the disturbance growth characteristics at the gas-liquid interfaces was formulated and validated, and a parametric study was performed to explore the mechanism that affects the sheet instability. The results reflect that para-sinuous disturbances on the liquid sheet always predominate over para-varicose disturbances under the considered flow conditions. The aerodynamic interaction at the gas-liquid interfaces of the liquid sheet is the decisive factor on sheet instability. As for the main factors affecting the aerodynamic effects, the contribution of the gas-liquid velocity difference to aerodynamic interactions is more significant than that of the gas-liquid density ratio. Neglecting the gas compressibility markedly underestimates the aerodynamic effects at the gasliquid interfaces for flow conditions of high gas Mach number, which results in decreased disturbance growth rate and dominant wave number. Moreover, both the liquid viscous force and the surface tension force hold back the disturbance growing and stabilize the liquid sheet under the considered conditions. Note that the destabilizing effect of the viscous force is limited for high liquid Reynolds number cases. In general, it is very necessary to consider the compressibility of the gas flows in the instability study of practical twin-fluid atomization. (C) 2019 Elsevier Ltd. All rights reserved.