The temporal inertial instabilities of the Type I Long’s vortex for large values of the flow force,M, are explored. It is found that growth rates and wave speeds obtained numerically for the exact vortex profiles agree very well with those obtained for large‐Mprofiles found by asymptotic means. Agreement is excellent, so the large‐Mstructure and inertial instability modes of the Type I Long’s vortex are now well established. It is determined that the modes computed here are ring modes. Both exact and asymptotic solutions display a spurious instability mode, which vanishes for increased resolution. ©1995 American Institute of Physics.