The vacuum gap-voltage oscillating characteristics in scanning tunnelling microscopy are calculated for a barrier between two plane electrodes. The transmittivity of the tunnel electrons, as well as the tunnel current, are calculated with and without the image potential. It is found that the image potential is important in determining not only the peak positions of the characteristics but also their shapes. Inelastic processes are also considered by using an optical potential. For zero applied voltage the oscillations in the transmittivity correspond precisely to the surface and image state resonances of the sample surface.