Hydrothermal uranium deposits are often closely associated with granites of abnormally high uranium content. We have studied the question as to whether the heat generated within such granites can cause fluid convection of sufficient magnitude to develop hydrothermal uranium deposits. Numerical models of flow through porous media were used to calculate temperatures and fluid flow in and around plutons similar to the Conway Granite, New Hampshire, i.e., with a half-width of 17 km, a thickness of 6.25 km, and a uniform internal heat generation rate of 20 X 10 (super -13) cal/cm 3 -sec. Fluid convection was computed for plutons with permeabilities between 0.01 and 5 millidarcies (1 X 10 (super -13) cm 2 to 5 X l0 (super -11) cm 2 ).Flow rates and the size and location of convection cells in and around radioactive plutons like the Conway Granite were found to depend critically on the permeability distribution within the pluton and in adjacent country rocks. The depth of burial, the distribution of heat sources within the pluton, and the small rates of heat generation in the country rock are only of minor importance. Topographic relief is unlikely to affect flow rates significantly but can have a major influence on the distribution of recharge and discharge areas.Within a few million years, the mass of water transported by steady state convection through such radioactive plutons can equal the mass of water which can convect through them during initial cooling from magmatic temperatures. If the permeability in a Conway-type pluton is on the order of 0.5 millidarcies, then the rate of fluid convection is probably sufficient to develop a hydrothermal ore deposit containing 10,000 tons of uranium in a period of two million years. Such a uranium deposit is most likely to develop in an area of strong upwelling or strong downwelling flow.