A finite element algorithm was developed to simulate wave propagation and near-source ground motion of propagating rupture fault. The modified ¡¥split-node¡¦ technique of Melosh and Raefsky was employed to simulate the equivalent body forces system for a double couple without moment. Synthetic seismograms were computed for a suite of dip-slip faultings with various slip directions, and rupture velocities to illustrate the ground motion and coseismic deformation variations. Results from this study showed that, for a thrust fault with infinite rupture velocity or down going propagating ruptures, the hanging wall has a stronger ground motion than the foot wall; in contrast, for up going or bi-lateral ruptures, the hanging wall has a weaker shacking than foot wall. For the propagating rupture faults, the ¡¥starting¡¦ and ¡¥stopping¡¦ phases were numerically reproduced using the finite element method. In addition, observation at the surface, the duration pulse of S-waves were significantly changed between both sides of the fault for the rupture directivity.