Both diffusion and effusion in radioactive ion beam foil targets can be described mathematically by Fick’s Law of diffusion. An approximate solution to the equation with the appropriate boundary conditions is presented for the RIST geometry target. This solution is expressed in terms of the physical and geometrical properties of the target and ioniser: the diffusion constant of the foil material, the conductance and the dimensions of the target and ioniser. The results of fitting the equation to measured data are shown. The equation can be used to optimize the design of targets for different radioactive ion beams. ©1999 American Institute of Physics.