The heat geueration and thermal stresses in spherical HRE-4 vessels 3 to 4 1/2 ft in diameter with clad and solid stainless steel walls were invegtigated. Parameters included thorium slurry concentrations and moderator material (D/sub 2/ O and H/sub 2/O). The prirnary purpose of this study was to determine the influence of thermal stresses on the selection of the core size for the HRE4 reactor. Curves are presented which facilitate relatively rapid determination of stresses for the range of vessels considered. It is concluded that steady- state thermal stresses in the clad or solid stainless steel vessels considered will not have to be a determining factor in the selection of a core size, provided the power density does not exceed approximately 15 kw/l in the clad vessels and 8 kw/l in the solid stainless steel vessels. (auth)