Seismograms are synthesized by super, postion of Gaussian beams for teleseismic S waves radiated by deep focus earthquakes located within the zone of high seismic velocities that define a descending lithospheric slab. The S wave synthetics demonstrate a phenomenon of slab diffraction that acts to lengthen the apparent pulse width of the S wave. Low-frequency energy leaks out of the slab and travels to the receivers along paths in the lower-velocity region surrounding the slab. Seismograms synthesized in fully three-dimensional models of slab structure show that slab diffraction strongly depends on the azimuth of the receiver with respect to strike of the slab. Slab diffraction lengthens the pulse width of S waves in the entire azimuthal range on the dipping side of the slab. As the azimuth approaches the strike of the slab, the diffracted phase may evolve into a higher-frequency, impulsive phase, which arrives after the minimum time arrival. Some slab models predict the slab phase to become a superposition of multipathed, ray theoretical arrivals as the azimuth approaches the strike of the slab. As the azimuth varies through the strike of the slab toward the side opposite the direction of dip, the slab phase is rapidly extinguished. Rapid variations in the complexity of S waveforms recorded along azimuths parallel to the strike of the slab are consistent with the predictions of synthetic seismograms. Evidence of slab diffraction in the S waveforms of the deepest focus earthquakes supports the hypothesis of slab penetration beyond 650 km depth. Broadband S waveforms from deep focus earthquakes in the Kuril-Kamchatka slab suggest that this slab penetrates below 650 km and that is may suffer some distortion in shape and advective thickening below this depth. ¿ American Geophysical Union 1989