  I consider the problem of vortex tunneling in a two-dimensional
superconductor. The vortex dynamics is governed by the Magnus force and the
Ohmic friction force. Under-barrier motion in the vicinity of the saddle point
of the pinning potential leads to a model with quadratic Hamiltonian which can
be analytically diagonalized. I find the dependence of the tunneling
probability on the normal state quasiparticle relaxation time $\tau$ with a
minimum at $\omega_0\tau\sim 1$, where $\omega_0$ is the level spacing of the
quasiparticle bound states inside the vortex core. The results agree
qualitatively with the available experimental data.
