Abstract: Translational ground motion is decomposed usually into three components: two horizontal components and one vertical component. As the maximum structure response may occur in any direction along the structure, usually the direction of the horizontal component, in which the maximum structure response occurs, is known as the critical orientation. The determination of the critical orientation is one of the key issues in bi-directional seismic excitation studies. In this paper, based on time history analysis results, a method is proposed to determine the critical angle of the structure response under a bi-directional seismic excitation as well as a graphic solution to the method. It is proved that for structures of linear elastic materials, this method gives exact solutions. In the meantime, the accuracy of the method for nonlinear-material structure is analyzed in this paper. The analysis shows that the method introduces an error increasing as the section strength reduction factor (Rd) grows, which stays below 10% while Rd is less than 6. It is shown that the structural response caused by the earthquake excitation in the critical angle of seismic incidence calculated by the proposed method is reasonably close to the maximum response in the random orientation of earthquakes.