The exact semiclassical wave function for a tunneling electron, coupled to the degrees of freedom of a host medium, is constructed. This permits a description of electron dynamics within the barrier. As a specific application, the result is used to calculate the tunneling amplitude for the electron interacting with the single vibrational mode of the medium. In agreement both with experiment and with previous numerical study two regimes of tunneling, i.e., polaron-type vibronic transport and superexchange, are found depending on the relationship of the Buttikker-Landauer tunneling time and the vibrational period. The evolution of the media interacting with the tunneling particle is described.