  Using a method of local transmission matrix, we generalize the well-known WKB
formula for a barrier penetrability to multi-channel systems. We compare the
WKB penetrability with a solution of the coupled-channels equations, and show
that the WKB formula works well at energies well below the lowest adiabatic
barrier. We also discuss the eigen-channel approach to a multi-channel
tunneling, which may improve the performance of the WKB formula near and above
the barrier.
