The effect of viscosity on the unstable interface of the cylindrical jet is analyzed through viscous potential flow approach. The jet is moving radially and jet interface is experiencing Rayleigh–Taylor type instability. Previous studies have completely ignored the viscosity effect while considering the instability of a radially moving cylindrical jet. The fluids inside and outside jet are incompressible as well as viscous. The theoretical analysis provides us a second-order ordinary differential equation to establish the instability/stability criterion. The radial velocity and acceleration both have significant impact on the stability of the jet. We found that as viscosity enters to the analysis, perturbations grow rapidly. In addition, the acquired stability criterion is applied to the cylindrical jets in HYLIFE-II which is basically an inertial confinement fusion reactor.