Convenient, economical epithermal neutron beams will be needed in the future for boron neutron capture therapy (BNCT). We studied two concepts for producing epithermal neutron beams with low-power reactors. The first design is a 100-kW reactor with a 235U fission plate placed outside the reflector region, plus an Al/Al2O3 moderator assembly. The beam, which is directed forward, delivers a flux of epithermal neutrons of 0.8 × 109 n/cm2·s and a fast neutron dose of 4.4 × 10−11 cGy·cm2/nepi. The second design is based on a slab reactor plus a similar Al/Al2O3 moderator assembly. With an operating power of 50 kW, the beam has an intensity of 1.4 × 109 n/cm2.s and a fast neutron dose of 4.6 × 10−11 cGy·cm2/nepi; this beam also is directed forward. These epithermal neutron beams should be acceptable for BNCT; a treatment could be completed in ∼1 h, and the fast neutron dose to the skin would not be the limiting dose. Such small reactors should be practicable in a hospital location.