Theoretical description of the electronic vibrational spectroscopy of atoms adsorbed on metal surfaces is developed which takes into account both open and closed (i.e. resonant) scattering channels of incoming electrons. Inelastic scattering cross section for the lowest order vibrational transition is formulated in the two-beam approximation, and the matrix elements are explicitly calculated in the point dipole model. The proper inclusion of the resonant channel scattering leads to the enhancement of the inelastic peaks near resonances, and, assuming the laterally screened induced electron-dipole interaction, explains the partial breakdown of the dipole selection rules and the relative strengths of parallel and normal vibrational excitations, as observed in HREELS of hydrogen adsorbed on transition metal surfaces. The angular dependences of the loss peaks on and off resonances are also discussed.