The viscous stability analysis of Long’s vortex is performed. Some quantitative disagreements with the inviscid results of previous investigators are reported. The truncation of the infinite radial domain into a small computational domain utilized in past investigations is found to be the source of these discrepancies. More important, for small flow forces, a type‐II Long’s vortex is shown to be destabilized by perturbations having positive azimuthal wave number. Based on previous numerical computations, it had been conjectured that these unstable eigenmodes may not exist. The stability characteristics of the unstable modes are fully mapped and are presented in detail.