The radiation swelling of materials is at present one of the main factors which limits the operating period of the fuel elements in fast reactors. The reason for the swelling is vacancies produced simultaneously with implantations in the primary event of elastic and also inelastic scattering of neutrons. Although this effect has been observed for a long time, it cannot be said that the mechanism of the phenomenon is sufficiently clear. The main difficulty in providing an explanation is due to the fact that the effect is many orders of magnitude less than the factors that give rise to it. Only tenths or hundredths of percent of all the vacancies produced remain in the material being irradiated and cause swelling. All the others disappear. There are different models of the process-one considers the pores formed as the nuclei of the second phase using the Gibbs-Folmer theory to describe the process, which is not entirely justified, while another postulates that there is some preference, i.e., a preferential disappearance of the inclusions when interaction occurs with inhomogeneities of the lattice, which is too artificial. In this paper, which has been prepared over a period of many years and has only now been finally completed, we attempt to construct a qualitative theory of the process based on simple and natural assumptions.We will start by assuming that, before being irradiated, the sample is an ideal single crystal with no defects. The actual presence of initial inhomogeneities of the lattice can, in principle, be regarded as unimportant, since defects rapidly arise in large numbers during irradiation. We will consider a certain region of a simple lattice containing a specified number of atoms at fairly far from the edges of the sample so that edge effects can be ignored. It is obvious that, when the sample is irradiated with the formation of each Frenkel pair, this region, as a result of the vacancy, will increase by an amount corresponding to a single atomic volume. The displacement of an atom, ejected from its position in the lattice into the interstices does not, in fact, have any effect on the size of the region.* The later fate of individual elementary defects which are formed and stored is determined by their interaction with one another and depends very much on the temperature of the sample. In this scheme, the whole available temperature range can be divided into two intervals: a low temperature range, where the defects are, so to speak, frozen, and a high-temperature range where the defects become mobile.