  In this work, the pulsation analysis is performed on 83 high-amplitude
$\delta$ Scuti stars, which have been observed by the Transiting Exoplanet
Survey Satellite (TESS). The results show that 49 of these HADS show
single-mode pulsation, 27 of them show radial double-modes pulsation (in which
22 of them pulsate with the fundamental and first overtone modes and 5 of them
pulsate with the first and second overtone modes), and 7 of them show radial
triple-modes pulsation (3 of which are newly confirmed triple-mode HADS). The
histogram of the fundamental periods and the ratios between the fundamental and
first overtone periods show bimodal structures, which might be caused by the
stellar evolution in this specific phase. Most of the radial triple-mode HADS
have a fundamental amplitude of 41-54 mmag, and 50% of them have similar
amplitudes of the fundamental and first overtone pulsation modes. All these
hints require further confirmation not only in observations with more HADS
samples, but also in theoretical models with suitable treatments of stellar
evolution and pulsation.
