Radioactivity and biological dose calculations have been performed for the target chamber of the Target Development Facility (TDF). Two conventional shield designs are considered. One has the target chamber submerged 3 m from the surface of a borated water pool, the other has the chamber surrounded by approximately 250 cm of concrete. The first wall materials, Al-6061 and 2-1/4 Cr-1 Mo steel and the ion beam targets, one made from BeO2 and W and the other from CH2 and Au, are investigated. Shielding designs are presented that reduce the dose from each of these choices of shield, first wall and target material to acceptable levels.