Using the Cagniard-de Hoop method we derive the particle velocity from an impulsive line source for transmitted SH waves through a boundary separating two homogeneous and solid half-spaces. With a series of examples the properties of the evanescent wave, such as their equivalent ray path and the decay with depth, are displayed as they would be recorded on a velocity transducer. It is shown that these waves should be prominent when either the source or the receiver is in the proximity of a boundary across which the acoustic impedance changes significantly. The amplitude decay of waves from a line source with distance far from the interface agrees well with the rate predicted by the asymptotic theory. Because of the appreciable amplitude when either source or receiver is near an interface, the evanescent wave is of importance in interpreting vertical seismic (VSP), hole-to-hole seismic data and in the understanding of synthetic seismograms.