A mathematical model describing steady state diffusion of radon-222 daughters, based on a uniform distribution of radon has been deveIoped. Solutions are generated for four coupled, non-homogenous differential equations satisfying the boundary conditions that the concentrations of all daughters vanish at the walls for cylindrical geometry. The solutions of these equations give the concentration of RaA, RaB, RaC and RaD as a function of the distance from the center of the containing vessel in terms of the diffusion coeficient, the radioactive decay constants, and the dimensions of the containment vessel. The results, integrated over the volume of the container and expressed as a fraction of the radon concentration, yield parent-daughter equilibrium values for cylinders of various dimensions.When the cylindrical geometry is used to approximate a uranium mine tunnel with a diameter of 8 ft, the model indicates that a significant parent-daughter disequilibrium exists using a value of the diffusion constant characteristic of unattached ions or atoms. Under aon-static conditions, convective or turbulent mixing would further decrease the daughter concentrations relative to radon due to an increased concentration gradient at the wall; however, the presence of aerosols would tend to reduce the rate of diffusion to the walls.