Nuclear design studies have been performed for two reactor-based epithermal neutron beams for cancer treatment by neutron capture therapy (NCT). An intermediate-intensity epithermal beam has been designed and implemented at the Brookhaven Medical Research Reactor (BMRR). Measurements show that the BMRR design predictions for the principal characteristics of this beam are accurate. A canine program for research into the biological effects of NCT is now under way at BMRR. The design for a high-intensity epithermal beam with minimal contamination from undesirable radiation components has been finalized for the Power Burst Facility (PBF) at the Idaho National Engineering Laboratory. This design will be implemented when it is determined that human NCT trials are advisable. The PBF beam will exhibit approximately an order of magnitude improvement in absolute epithermal flux intensity over that available in the BMRR, and its angular distribution and spectral characteristics will be more advantageous for NCT. The combined effects of beam intensity, angular distribution, spectrum, and contaminant level allow the desired tumor radiation dose to be delivered in much shorter times than are possible with the currently available BMRR beam, with a significant reduction (factor of 3 to 5) in collateral dose due to beam contaminants.