A detailed theory of planar electron channelling radiation, based on the theory of high energy electron diffraction, is presented to explain the experimental results of Swent et al. (1979). Provided the photon energy is small compared with the electron rest mass it is shown that the radiation cross section is equivalent to that from a classical oscillator moving relativistically. Quantum mechanics is important only for the transverse motion, the energies of the observed peaks in the frequency spectrum being determined by the spacings of the transverse energy levels bound in the planar channelling potential. The mechanisms that lead to the observed width of the peaks are also discussed. For high energy photons the main cause is de-channelling whereas for the lower energy photons, band-structure effect due to tunnelling between adjacent wells can become important.