Radon is a noble gas capable of permeating microscopic imperfections such as crevices, pores and structural failures in materials (Cothern and Smith, 1987; Culot et al, 1976). This represents a serious problem if a control of the radon levels between the soil and the basements of buildings; is to be achieved by intervening radium impervious barrier. In order to understand the behavior of radon in this respect, we have measured the relative radon permeability of a number of materials: polyethylene of differents thicknesses, various paper materials, aluminum foils and mylar using solid state nuclear track detectors. The results of our experiments provide some insight into the required properties for the better barrier materials for controlling the indoor levels of radon.