Problems of burnup of nuclear fuel elements are treated. The factors which determine the percentage of fissionable material; in a nuclear fuel destroyed by fission or capture are reviewed and analyzed. The elements, for failure from core or fuel element design, fabrication defects, and reactor operating conditons, are analyzed. Suggestions for improving the burn-up are given. It is further proposed to collect data for an Atlas of Fuel Elements and Their Burn-up Relations.'' An example for this "Atlas" is given itn the appendix describing the fuel elements in the BNL-1 reactor and their performance. Attempts have been made to correlate fuel element performance with design. (auth)