A theoretical study of the ground motion produced by strike slip faults is presented. The source is modeled as a progagating dislocation embedded in a layered medium. The resulting surface displacement is computed at more than a thousand locations covering the whole near-source region (0--100 km from the source). The seismograms obtained are then combined together to yield the space and time dependence of the ground motion. Various source-medium configurations are studied. The results show the strong directivity effect of the propagating rupture. Large surface displacements and high-frequency motions are confined to a narrow zone around the fault and to the region which extends beyond the source along the trend of the fault. SH waves and Love waves are the dominant contribution to the ground shaking. The vertical displacement is small but exhibits high-frequency oscillatory motions. The presence of low-velocity surface layers has a very severe effect on the amplitude and duration of the ground shaking.