  We have investigated that the Goos-H\"anchen (GH) shifts in frustrated total
internal reflection (FTIR) studied with wave packet propagation. In the
first-order approximation of the transmission coefficient, the GH shift is
exactly the expression given by stationary phase method, thus saturates an
asymptotic constant in two different ways depending on the angle of incidence.
Taking account into the second-order approximation, the GH shift always depends
on the width of the air gap due to the modification of the beam width. It is
further shown that the GH shift with second-order correction increases with
decreasing the beam width at the small incidence angles, while for the large
incidence angles it reveals a strong decrease with decreasing the beam width.
These phenomena offers the better understanding of the tunneling delay time in
FTIR.
