  We consider the upward-going muon flux due to the WIMP annihilations in the
cores of the sun and the earth, including the upper bound on the branching
ratio for $B_s \to \mu^+ \mu^-$ decay. We find that the constraint from $B_s
\to \mu^+ \mu^-$ is very strong in most parameter space, and exclude the
supergravity parameter space regions where the expected upward-going muon
fluxes are within the expected reach of AMANDA II.
