One of the pressing problems of the potential nuclear-power industry is the necessity for disposing of radioactive wastes incident to operating reactors and recovering fissionable material from expended fuel elements. The Bureau of Mines has made a detailed analysis of the feasibility of solving this problem in areas where the geology permits by injecting liquid wastes into shallow, permeable, sedimentary rock formations. General considerations pertinent to the disposal of radioactive wastes are reviewed. Suggested methods of disposal, geographical influences, and the factors pertaining to shipping liquid and solid radioactive wastes are discussed. Current practices of the oil industry in the United States in disposing of oil-field brines are reviewed. The economics of brine injection is compared to present costs of storing and estimated costs of disposing of high-level radioactive wastes. A comparison is made of the current costs of drilling wells to different depths; the relative economics of drilling exploratory, injection, and monitoring wells to different depths in a disposal or test project is discussed. The geology of comparatively shallow and stratigraphically isolated sandstone lenses and shoestrings common to midcontinental United States is considered. Particular emphasis is given to the geological, engineering, and chemical information available about such formations that have been proved to be productive of petroleum and have been repressured with fluids to stimulate oil production. Laboratory and field research problems pertinent to the disposal of radioactive wastes by injection are outlined. Laboratory problems include ion exchange and adsorption of fission products, chemical and physical reactions between injected wastes and reservoir solids and fluids, corrosivity of wastes and corrosion resistance of special metallic alloys, injectivity of solutions of waste fission products, potential heat gradients, and techniques for determining migration of injected wastes. Field research problems include handling techniques, injectivity, and horizontal and vertical migration of injected radioactive wastes. A hypothetical example is given of a pilot plant for secondary treatment and injection of dilute fission products into a shallow, lenticular sandstone formation with well-defined boundary conditions. Monitoring facilities and techniques designed to determine horizontal and vertical migration and differentiation of the migrating radioisotopes are described. A partial cost analysis is made of the pilot system. The advantages and disadvantages of a full-scale system of this type, as compared with other methods of disposal are discussed. It is concluded that the use of shallow sedimentary formations, including partly depleted oil-productive sands, for disposing of radioactive wastes in some areas where geology permits, is feasible and that field pilot plants to demonstrate that feasibility might be instituted with information available at this time.