Radon is an inert radioactive gas released into the atmosphere from certain minerals and man-made products in which it is produced. It can accumulate in confined spaces. Radon emanation into a building can come from: the underlying soil, the building materials, tap water and natural gas. The principal isotope, 222Rn, decays to products which if inhaled can result in exposure of the respiratory tract to alpha radiation. The decay products, radon daughters, are significant because of their potential to cause health effects. In this study we present measurements of radon concentration, and the internal and external gamma dose to which the inhabitants of a housing block with ten floors are exposed. Solid State Nuclear Track Detectors (CR-39) were used for the determination of radon concentration in the air. LiF (TLD-100) dosimeters were used for measuring the external gamma dose. Of the total equivalent dose to which people are exposed, it appears that from inside the building makes the greatest contribution.