Global stability analysis by time-stepping approach with a thermochemical nonequilibrium code was conducted for hypersonic flows around the HIFiRE-1 model under conditions of the HIEST experiments. The flowfields were unstable for all the conditions as expected, and characteristic structures were extracted as an eigen-mode corresponding to the largest real eigenvalue. The structures obtained on the edge of the boundary layer are periodic and have the features of the second mode. The frequency of pressure fluctuation on the wall also indicates prominence of the second mode, while it is different in a factor of 100 kHz from the experimental data. Another periodic structure like the second mode is also found in the middle of the shock layer, and turbulent transition points observed in the experiments are located close to the points influenced by this structure via acoustic waves. Moreover, this periodic structure may result from the interference between the acoustic waves emitted from the second mode and the shock surface.