  Quantum tunneling from a thin wire or a thin film through a static potential
barrier in a zero magnetic field is studied. The wire or the film should
satisfy a condition of transverse quantization of levels and be inhomogeneous.
Depending on a form of the inhomogeneity the tunneling scenario can
dramatically differ from the conventional scheme of an exponential decay of a
probability density inside the barrier. This happens due to interference of
various underbarrier paths, which are collected at some points giving rise to a
trans-barrier state of a large amplitude. As a result, the tunneling
probability through an almost classical barrier can be not exponentially small.
This is a phenomenon of Euclidean resonance studied earlier for tunneling
across nonstationary barriers.
