The global stability analysis (GSA) is conducted for a supersonic flow over a hollow-cylinder/flare configuration at Mach 2.25. Special emphasis is placed on the impact of axisymmetric effects on global instability with different cylinder radii. The stable hollow-cylinder/flare flow becomes unstable with increasing flare angles. Besides, the increase in flare angles results in more unstable modes. The captured modes resemble unstable modes previously observed in compression corner flows. Secondary separation and global instability are postponed as the cylinder radius is decreased. A global stability boundary is proposed for hollow-cylinder/flare flows to estimate the occurrence of global instability using triple-deck scaling.