Radon ²²²Rn is known to diffuse through porous building materials like concrete, cement, paints, etc. Consequently, radon from soil or building materials may penetrate floors or concrete shelter walls and accumulate in dwellings. Buildings and shelters should have floor and wall materials or membrane coverings such as to block radon penetration. The choice of membrane and its thickness depends among other factors (environmental stability) on its radon diffusion length (L), the distance through which the radon concentration decreases to 37% of its original value. We measure L with a setup consisting of chambers 1 and 2 with volumes V₁ and V₂ , separated by the thin membrane of area S and thickness ℓ. Chamber 1 contains a radon source of activity A_S. We use a mathematical model describing the steady state radon diffusion from chamber 1 to 2. Knowledge of A_S, V₁, V₂, ℓ, S and direct measurement of the steady state radon concentrations C₁ and C₂ in chambers 1 and 2 allows determining the diffusion length L by iteratively solving the appropriate diffusion equation. We carry out these measurements as part of an international comparison of Radon diffusion length measurements of polymer foils organized by the National Radiation Protection Institute of Prague, Czech Republic. Experimental methods, theoretical background, and preliminary measurement for a variety of membranes will be presented. Our final results are planned for presentation  in Prague at the Sept. 2010 6th Conference on Protection Against Radon at Home and at Work.