We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation-hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by (M) over dot(r) = eta(L-*/c(2))(r/R)(2)(Delta R/R)(1 - e(-tau)) at radius r, where the efficiency eta ranges from 0.2 up to 1, L-* and R are respectively the bolometric luminosity and the radius of the starburst ring, Delta R is the extent of the emission regions, and tau is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to similar to parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation-hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.