A temporal stability analysis was carried out to model the atomization of a swirling viscous annular liquid sheet emanating from an air-blast atomizer subject to inner and outer inviscid swirling air streams. The dimensionless dispersion equation that governs the instability of a viscous Non-Newtonian annular liquid sheet under swirling air streams was derived. In order to investigate the effects of the ratio liquid/ gas flow on the maximum growth rate and its corresponding unstable wave number, numerical solutions of the dispersion equation, under a wide range of viscosities and flow conditions were obtained.