  Using the neutrino telescope AMANDA-II, we have conducted two analyses
searching for neutrino-induced cascades from gamma-ray bursts. No evidence of
astrophysical neutrinos was found, and limits are presented for several models.
We also present neutrino effective areas which allow the calculation of limits
for any neutrino production model. The first analysis looked for a statistical
excess of events within a sliding window of 1 or 100 seconds (for short and
long burst classes, respectively) during the years 2001-2003. The resulting
upper limit on the diffuse flux normalization times E^2 for the Waxman-Bahcall
model at 1 PeV is 1.6 x 10^-6 GeV cm^-2 s^-1 sr^-1 (a factor of 120 above the
theoretical prediction). For this search 90% of the neutrinos would fall in the
energy range 50 TeV to 7 PeV. The second analysis looked for neutrino-induced
cascades in coincidence with 73 bursts detected by BATSE in the year 2000. The
resulting upper limit on the diffuse flux normalization times E^2, also at 1
PeV, is 1.5 x 10^-6 GeV cm^-2 s^-1 sr^-1 (a factor of 110 above the theoretical
prediction) for the same energy range. The neutrino-induced cascade channel is
complementary to the up-going muon channel. We comment on its advantages for
searches of neutrinos from GRBs and its future use with IceCube.
