  We present the results of numerical calculations on propagation of
Extremely-high energy (EHE) neutrinos and charged leptons in the earth for
trajectories in all phase space of nadir angles. Our comprehensive calculation
has shown that not only the secondary produced muons but also taus survive
without decaying in energy range of 10PeV-100PeV with intensity approximately
three orders of magnitude lower than the neutrino flux regardless of EHE
neutrino production models. They form detectable horizontal or downgoing events
in a 1km$^3$ underground neutrino telescope such as the IceCube detector. The
event rate and the resultant detectability of EHE signals in comparison with
the atmospheric muon background are also evaluated. The 90 % C.L. upperlimit of
EHE neutrino fluxes by a km$^2$ detection area would be placed at $E^2dF/dE
\simeq 3.7\times 10^{-8}$ GeV/cm$^2$ sec sr for $\nu_{\mu}$ and $4.6\times
10^{-8}$ for $\nu_{\tau}$ with energies of $10^9$ GeV in absence of signals
with energy-loss in a detection volume of 10PeV or greater.
