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.