We have simulated a rupture transition from quasi-static growth to dynamic propagation using the boundary integral equation method. In order to make a physically reasonable model of earthquake cycle, we have to evaluate the dynamic rupture propagation in the context of quasi-static simulation. We used a snapshot of the stress just before the earthquake in the quasi-static simulation. And the resultant stress will be feedbacked to the quasi-static simulation. Since the quasi-static simulation used the slip and state dependent friction, friction law itself evolves with time. Thus we used the constitutive relation for dynamic rupture propagation consistent with that used for the quasi-static simulation. We modeled the San Andreas type strike slip fault, in which two different size asperities existed.