  The effect of inelastic scattering on quantum tunneling through a rectangular
potential barrier, of length $L$, containing randomly distributed impurities,
is considered. It is shown that, despite the fact that the inelastic transition
probability $\mathcal{T}_{\mathrm{inelastic}}$ is exponentially small, it may
be greater than that of the elastic in the out of resonance conditions for some
energy interval $\triangle E$ (the energy of the incident particle is far from
the spectrum of the random Hamiltonian). The asymptotic of the tunnelling
transition probability for various impurity configurations are found and the
energy interval $\triangle E$ where
$\mathcal{T}_{\mathrm{elastic}}\sim\exp(-L/L^{*})\lesssim\mathcal{T}_{\mathrm{i
nelastic}}$ is determined.
