Research of the aftershock activity base on static stress triggering has two main aims: to discuss about how mainshock triggers aftershocks，and to find the qualitative relationship between coulomb stress distribution and the actual spatial distribution of aftershocks． It is generally believed that aftershocks occur in the area in which the coulomb stress change is right． This is an important evidence of the relationship between the stress changes and aftershock activity． In the research of aftershock prediction based on the stress change，one important method is the rate- and state-dependent friction law． It regards the aftershock activity as a series of separate “earthquake nucleation”events，and based on the theory of fault slip triggering earthquakes，it gets the aftershock activity rate from static stress change，and the number of aftershocks as a result． Aftershock activity is associated with shear stress change on the faults， and seismicity rate changes depend on the amplitude of stress disturbance，the stressing rate，the physical constitutive properties of faults ( represented by the parameter Aσ)，and the background seismicity rate of the study area． The statistical self-similar characteristics of aftershocks in ETAS model may provide an approach to describe the aftershock activity more precisely using both statistical and physical ( stress change) method．