Using 3D finite difference code developed by Dr. Day in SCEC, we simulated fault dynamic rupture process and associated near-fault strong ground motion for the 1976 M(s)7.8 Tangshan earthquake based on a simplified bi-lateral rupture model and slip-weakening frictional law. The fault length, width, and depth of the model are 200 km, 140 km, and 40 km, respectively. The discretized space and time steps are 200m and 0.012 s, respectively, which make the total number of node points up to 0.15 billion. In the implementation level, a parallel computational algorithm has been developed in DELL work station, and a computer visualization technique has been used in the numerical simulation in order to do data analysis. Furthermore, a regional 3D velocity model also has been embedded into the model to simulate seismic wave propagation and associated ground motion. According to the numerical results we discussed the characteristics of the ground motions produced from the 3D rupture model with associated 3D velocity structure, including PGA and PGV distributions around fault. A physics based explanation related to the rupture directivity is also proposed to show that the radiated SH-type particle motion (fault-normal component) from ruptured fault has a significant influence on the near fault ground motion along the fault strike direction. Based on the radiated SH wave motion and propagation caused by directivity effect, we proposed that, for the 1976 M(s)7.1 Luanxian and M(s)6.9 Ninghe earthquakes, a dynamic triggering mechanism related to the temporal stress variation could play a significant role to trigger these two events. The result shows that the dynamic stress change could reach 2 similar to 3 MPa in strike direction and 0.1 similar to 0.2 MPa in thrust direction.