Because the Earth’s outer core is liquid, shear waves generated by a large earthquake that travel to the core (ScS) are totally reflected with strong seismic energy. It is interesting to note that one large aftershock (M_w 6.0) of the 2008 Wenchuan earthquake (M_w 7.9) in China occurred when the ScS phase returned around 15.5 m after the mainshock. Estimated peak dynamic stress (∼3.3 kPa) of the ScS amplitude reaches the critical level of the lower boundary capable of triggering earthquakes. Both the temporal correlation between aftershock occurrence and ScS arrival, as well as the dynamic stress capable of triggering an earthquake, suggest that the large aftershock might well have been triggered dynamically by ScS waves. A similar feature of another large aftershock (M_b 5.3) occurring around the time of ScS arrival has been also found from the 2003 Hokkaido earthquake (M_w 8.3). Further statistical examinations of 25 major earthquakes (M_w>8.0) between 1994 and 2008 shows some large aftershocks (M_w>5.0) also occurring around the time ofScS-phase arrival. It is reasonable to conclude that these observations suggest aftershocks being triggered dynamically by ScS-phase arrivals, and thus a temporal warning for potentially destructive aftershocks might be considered for future great earthquakes.