  We investigate the depinning of a massive elastic manifold with $d$ internal
dimensions, embedded in a $(d+n)$-dimensional space, and subject to an
isotropic pinning potential $V({\bf u})=V(|{\bf u}|).$ The tunneling process is
driven by a small external force ${\bf F}.$ We find the zero temperature and
high temperature instantons and show that for the case $1\le d\le 6$ the
problem exhibits a sharp transition from quantum to classical behavior: At low
temperatures $T<T_{c}$ the Euclidean action is constant up to exponentially
small corrections, while for $T> T_{c},$ ${S_{\rm Eucl}(d,T)}/{\hbar} =
{U(d)}/{T}.$ The results are universal and do not depend on the detailed shape
of the trapping potential $V({\bf u})$. Possible applications of the problem to
the depinning of vortices in high-$T_{c}$ superconductors and nucleation in
$d$-dimensional phase transitions are discussed. In addition, we determine the
high-temperature asymptotics of the preexponential factor for the
$(1+1)$-dimensional problem.
