It is assumed that when a hole appears in the cladding of a reactor fuel tube the fission products in the space between the fuel and the cladding will diffuse towards the hole. There they are swept away by the flow of steam past the hole. The process of diffusion is assumed to be governed by the ordinary diffusion equation with the boundary condition that the density of the fission products is zero at the surface of the hole. The diffusion equation is solved for the case of steady-state emission for a number of geometrical arrangements: long slit in plane surface; long slit in cylindrical surfaces circular hole in plane surface; circular hole in cylindrical surface; hole at end of cylindrical fuel rods and diffusion space of variable thickness. The time dependent solution of the diffusion equation is also found for a planar diffusion space. The effect of a temperature gradient is discussed.