The 2011 Great Tohoku Earthquake with Mw 9.0 that occurred off the Pacific coast of Japan was a multi-segment earthquake. Although the earthquake source was from one ruptured point, numerous ground motion patterns were produced because of differences in the orders and time intervals of the occurrences. As such, predicting multi-segment earthquake waves needs sophisticated expertise and great deal of effort. Even if they are accurately predicted, evaluating the response of high-rise buildings to multi-segment earthquakes is complex.<br> Now, measures have been carried out to protect high-rise buildings against the long-period ground motions for the Nankai trough multi-segment earthquakes. One widely adopted measure is incorporating dampers in the design of high-rise buildings to reduce seismic responses for long-period ground motions.<br> Proposed by previous researchers is a seismic evaluation method for seismic structures subjected to multi-segment earthquakes by considering the single earthquakes constituting them. With a possibility that this type of earthquake will occur in Japanese coastal waters, this current study developed a method for evaluating damped high-rise building subjected to multi-segment earthquakes.<br> Chapter 2 of this paper discusses the ground motion of multi-segment earthquake and the earthquakes constituting it. The ground motion of Tokai-Tonankai-Nankai multi-segment earthquake estimated by past researchers is used in this study. This long-period ground motion is simulated using a three-dimensional (3D) subsurface ground model for the Kanto, Nobi and Osaka plains.<br> The 50-story steel vibration control building models with dampers used in this study and response evaluation are discussed in Chapter 3. In Chapter 4, the time-history analysis of building models for the multi-segment earthquake and for the single constituting earthquakes are discussed. Results are compared to analyze the maximum response and cumulative damage for multi-segment earthquake.<br> Chapter 5 expands the seismic evaluation method of past researchers into the prediction method for damped structures subjected to multi-segment earthquake based on the response from the single constituting earthquakes. The maximum response produced by the multi-segment earthquake can be estimated by increasing the ground motion of the single constituting earthquake to the provisional multi-segment earthquake level based on an adjustment factor before the seismic response analysis. This adjustment factor (as in previous researcher) is the ratio of the greatest single constituting earthquake spectrum to the SRSS spectrum of the single earthquakes. The cumulative damage is estimated by summing up the energy of individual earthquakes and applying the energy balance-based seismic response evaluation method. The results of the seismic response analysis show that these estimation match well the responses produces by multi-segment earthquakes.<br> Finally, the method and procedure to predict maximum response and cumulative damage for multi-segment earthquake by single earthquakes are proposed in Chapter 6.