We have obtained numerical results for an acoustic wave propagating in a 3D medium with mixed boundary conditions. The specific model involves a vertical low-velocity fault zone of varying thickness embedded in an otherwise homogeneous half-space. At the fault-zone boundary, the stress and displacement are continuous; on the free surface, the stress is zero. A pseudo-spectrum method is employed to achieve sufficient resolution with reasonable computation time on a CRAY. Results show the development of guided waves trapped in the fault zone. These guided waves display large amplitudes and lengthening waveforms; they propagate at lower velocity with amplitudes that drop off mainly due to energy leakage out of the fault zone. As the width of the fault zone varies, the wave energy tends to funnel into the new low-velocity wave guide. At large distance, these guided waves become the dominant arrivals on seismograms. The waveforms are useful to recover the geometry and properties of the fault zone.