To reveal the failure mechanism of long-period structures, we obtained the instant energy spectrum by the Hilbert-Huang transform (HHT), and analyzed the structure's displacement response based on the theory of simple harmonic seismic response. The transient response of a MDOF system was also calculated based on a harmonic earthquake response analysis. Notable characteristics on long-period structures were different from short-period structures, based on analyses of the transient vibration patterns of a long-period (e.g., 15 layer) building. First, the time of peak displacement response on the structure was always observed to be later than the time of peak value of earthquake energy. Second, the displacement response was mainly controlled by the transient response in low order modals. Third, the first order modal displacement hysteresis lasted the longest, and the hysteresis mainly depended on the natural vibration period of the structure. The conclusions showed that demolition and collapse of long-period structures due to the strong earthquake did not happen at the greatest density of earthquake ground motion.