During a 4-month period starting from 21 January, 1997, an earthquake swarm of seven major events (Ms≥6.0) struck the Jiashi region at the northwestern corner of the Tarim Basin in Xinjiang,, China. Previous relocation studies suggested that these strong earthquakes had occurred along at least two parallel rupture zones. According to the relocated hypocenters and focal mechanisms of the events, we have constructed fault models for these seven earthquakes to calculate the Coulomb stress changes produced by each of these events. Furthermore, we extended our model calculations to include an ad- jacent 1996 Ms=6.9 Artushi earthquake, which occurred one year before the Jiashi earthquake swarm. Our calculations show that the Coulomb stress change caused by the preceding events was around 0.05 MPa at the hypocenter of the 4th event, and higher than 0.08 MPa at the hypocenters of the 2nd, 3rd, 5th and 6th events. Our results reveal a Coulomb stress interactive cycle of earthquake triggering between two adjacent normal and strike-slip faults.