  Some supersymmetric models predicted long lived charged sleptons. Following
Albuquerque, Burdman and Chacko \cite{albu}, we consider an exact process where
the $ \widetilde{\tau}$, the supersymmetry partner of $\tau$ lepton, are
produced inside the earth by collisions of high energy neutrinos with nucleons.
We detailedly investigate the possible signals of upgoing $ \widetilde{\tau}$
by comparing with the background muons where atmospheric neutrino flux is taken
into account. The realistic spectra shows that km-scale experiments could see
as many as 69 events a year by using the Waxman-Bahcall limit on the
extraterrestrial neutrino flux.
