The stability of a cylindrical interface separating two incompressible, inviscid and immiscible fluids under the action of radial motion is studied. Linear stability analysis is employed to understand the destabilization characteristics of the two fluid interface.Three-dimensional as well as two-dimensional (axisymmetric and azimuthal) disturbances are separately considered in the presence of surface tension. A dispersion relation governing this problem is taken from literature and analyzed. The relevant dimensionless parameters governing this study are Bond number, radial Weber number and density ratio. This dispersion relation permits the consideration of two different scenarios: (1) density of the inner fluid being greater than the outer fluid and (2) density of the inner fluid being lesser than the outer fluid. It is found out that the surface tension restricts and aids the destabilization for the former and latter case, respectively. It is also observed that the interface is unstable when even at a constant radial velocity. This is contrary to our common understanding of Rayleigh–Taylor instability where acceleration is required. Three destabilization modes are identified namely Taylor (axial) mode, flute (azimuthal) mode and helical (three-dimensional) mode for a range of parameters. It is found that three-dimensional modes are more susceptible to destabilization than the two-dimensional modes when the radial Weber number is close to zero. Regime maps are created in the Bond number, radial Weber number and density ratio space to establish the regimes where different modes occur. For a given density ratio, the destabilization starts from one mode to another two-dimensional disturbance through three-dimensional disturbances. The second and utmost finding of this study reveals that radial Weber number alone (albeit the Bond number) is sufficient to destabilize a cylindrical interface. © 2019, Springer Nature B.V.