Teleseismic SV waves have been generally ignored in wave propagation and source studies because of known complications in wave propagation for structure near the source and near the receiver. The validity of common optic ray and WKBJ seismogram methods for computing SV synthetic seismograms is examined by computing synthetic seismograms using these techniques and comparing them to SV synthetics produced from a wavenumber integration technique. Both ray methods give a poor approximation to the wave propagation for distances less than 60°. Diffracted Sp and the SPL wave interfere with near-source phases, such as S, pS, and sS for a shallow seismic source, producing anomalously high amplitudes and complex waveforms in agreement with observational experience. Because of the Moho Sp and diffracted Sp phases, the vertical component of motion shows greater distortion, relative to the ray theory result, than does the radial component of motion. Ray theory appears to be appropriate for the initial 20 sec of the SV wave train from a shallow source for ranges greater than 60°. SV waves from deep sources are less affected by diffracted Sp and SPL than SV from shallow sources.