Atomic hydrogen regions have been observed in λ21-cm emission around a number of galactic HII regions in various stages of evolution (Roger & Pedlar, 1981; Dewdney & Roger, 1982; Roger & Irwin, 1982). These HI zones are almost certainly formed by the dissociation of H2 with Lyman-Werner band photons in the UV from the exciting stars. We describe some results of the computer modelling of the advancement of dissociation fronts with time as functions of various parameters, principally stellar type and ambient gas density. The modelling has shown that for most conditions a substantial HI zone is formed fairly rapidly around a new star. When the dissociation front moves out to a distance where absorbing molecules are predominantly in the ground vibrational state, further advancement of the front is much slower.