  We study the stability of the electroweak vacuum in the supersymmetric (SUSY)
standard model (SM), paying particular attention to its relation to the SUSY
contribution to the muon anomalous magnetic moment $a_\mu$. If the SUSY
contribution to $a_\mu$ is sizable, the electroweak vacuum may become unstable
because of enhanced trilinear scalar interactions in particular when the
sleptons are heavy. Consequently, assuming enhanced SUSY contribution to
$a_\mu$, an upper bound on the slepton masses is obtained. We give a detailed
prescription to perform a full one-loop calculation of the decay rate of the
electroweak vacuum for the case that the SUSY contribution to $a_\mu$ is
enhanced. We also give an upper bound on the slepton masses as a function of
the SUSY contribution to $a_\mu$.
