Noticeable unrelaxed axial tension-not considered in previous studies-persists for long distances along the viscoelastic annular liquid sheet when it issues from the nozzle. Axial tension can significantly influence the instability behavior of viscoelastic sheet. Viscoelastic annular liquid sheets, subjected to unrelaxed axial tension and moving in a co-flowing gas medium, are investigated here. The dispersion relation between unstable growth rate and wave number is derived by temporal stability analysis. The effects of various parameters on the instability of annular sheets, when the axial tension cannot be ignored, were examined in the para-sinuous mode. This analysis proves that viscoelastic annular liquid sheets with reasonable parametric values can behave with greater stability than corresponding Newtonian sheets. The effects of the elasticity number and the Ohnesorge number on the unstable growth rate differ in cases with and without axial tension; however, the influence of the time constant ratio, gas-to-liquid density ratio, and gas-to-liquid velocity ratio on the instability of sheet are analogous, whether or not axial tension is taken into account. The effects of the velocity difference across each interface, and the co-flowing gas streams on the maximum growth rate, are also discussed here. (C) 2013 Elsevier B.V. All rights reserved.