When conducting the seismic response analysis on a long elevated structure, if the transmitting boundary is set at both ends of the analysis region, there is a condition that the response becomes larger than in the case of the free boundary. In this research, we studied the influence of the effective duration time of earthquake motion on the maximum displacement amplitude of earthquake response and the response energy of earthquake when carrying out similar analysis using viscous boundary. As a result, it was confirmed that the correlation between the effective duration and the relationship between the viscous boundary and the maximum displacement amplitude ratio of the free boundary is low. On the other hand, for the relationship between the effective duration time and the response energy ratio between the viscous boundary and the free boundary, the variance was small and a certain correlation was confirmed.