Radio spectra of radio galaxies are often ascribed a simple power law form (S-v proportional to v(alpha)) with the spectral index, alpha, being approximately -0.7. However, all radio galaxies deviate from this simple power law behaviour. In this paper we derive simple expressions for the average rest-frame spectra of FRI and FRII radio galaxies. These will be used to describe the spectral curvature of the parent (FRI and FRII) populations in models of radio source evolution.