[en] A simple model has been developed for the dispersion of radioactive materials in a closed and finite ocean. It allows for the simultaneous action of both diffusion and horizontal (but not vertical) advection, and thus avoids the major limitations of previous models such as that of Webb and Morley. It is sufficiently versatile to handle non-Fickian diffusion and radioactive decay, but requires numerical integration using some semi-empirical form for the Green's function of diffusion from a point source. The model has been used to estimate equilibrium concentrations of radioactive materials in sea water arising from the continuous release of material from a dump on the bottom of the deep ocean, using parameters appropriate for the North Atlantic. It is found that except under rather extreme conditions the surface concentrations do not exceed the long-term average value which would be established in a perfectly mixed ocean. The concentrations are also rather insensitive to the values of the diffusion and advection parameters used, except for that for vertical diffusion, but depend strongly on the overall removal rate of material from the ocean, including processes other than radioactive decay. It is suggested that safety assessments of deep-sea dumping should utilize estimates of the environmental capacities of the oceans based on the long-term 'well-mixed' average concentrations (which are very easily calculated) using a safety factor of no more than ten to allow for the possible effects of pluming and upwelling. In so far as their results are comparable, the present model yields estimates which are close to those of the Webb-Morley model for overall half-lives between 30 and 3000 years, but which become increasingly more restrictive for longer-lived materials. (author)