  We calculate low scale gravity effects on the cross section for
neutrino-nucleon scattering at center of mass energies up to the
Greisen-Zatsepin-Kuzmin (GZK) scale, in the eikonal approximation. We compare
the cases of an infinitely thin brane embedded in n=5 compactified
extra-dimensions, and of a brane with a physical tension M_{S}=1 TeV and
M_{S}=10 TeV. The extra dimensional Planck scale M_{D} is set at 10^{3} GeV and
2\times10^{3} GeV. We also compare our calculations with neutral current
standard model calculations in the same energy range, and compare the thin
brane eikonal cross section to its saddle point approximation. New physics
effects enhance the cross section by orders of magnitude on average. They are
quite sensitive to M_{S} and M_{D} choices, though much less sensitive to n.
