Abstract: This paper investigates structural response characteristics in the consideration of the directional uncertainty of earthquake ground motions. For this purpose, a simple 3-dimensional model is established. In elastic range, Maximum Bilateral Acceleration Response (MBAR), accounting for the variation of imposing directions of earthquakes, is compared with the unilateral one (UAR) based on the analysis of 2-dimensional model subjected to a unilateral earthquake excitation, to evaluate the effect of directional uncertainty in earthquake excitations. In plastic range, Maximum Bilateral Displacement Response (MBDR) is compared with the bilateral one (BDR) and the unilateral one (UDR). The results show that, on average, MBAR is 1.08 times larger than UAR; MBDR is 1.12 times larger than BDR and 1.15 times larger than UDR. At last, a statistical analysis yields magnification factors. Magnifying UAR, UDR and BDR with the corresponding magnification factor will guarantee a probability of 95% design safety.