Abstract: Only the action of horizontal earthquake was considered generallywhen structure with MRD was analyzed.The correlation of movements in horizontal and vertical directions wasnot well studied.This paper considers the structure with MRD under bidirectional couplingearthquake. The dynamic analysismodel is set up, kinetic differential equations are obtained,and dynamic time history analysis is made. Taking an 8-story structurewith MRD for example, the results show that the seismic responses of thestructure with MRD increase in some extent under the action ofearthquake in vertical direction. Therefore, it is highly recommended thatthe influence of vertical earthquake action on such structures should betaken into account in high-intensity earthquake regions. The optimal modelfor structures with MRD is set up. The various earthquake responses ofstructures with MRD under various loading conditions can be bettercontrolled after the optimization with IHGA.