Computational studies are performed for choosing an optimal material and dimensions of a moderator for forming a beam of epithermal neutrons for boron-neutron-capture therapy based on a proton accelerator and the reaction 7 Li(p, n) 7 Be as the neutron source. It is shown that the best material for this is magnesium fluoride. An optimal configuration is proposed for a combined moderator consisting of magnesium fluoride and teflon. The computational results are compared with the experimental data.Neutron capture therapy, whose fundamental feature is selectivity of the radiation damage to cancer cells, is now regarded as a promising method for treating certain malignant tumors, specifically, various forms of brain tumors. Although the therapeutic effect in this method is based on the radiation action of the products of nuclear reactions, produced by thermal neutrons in strongly neutron-absorbing nuclides, such as 10 B and 157 Gd, the low penetration power of thermal neutrons in tissue limits their application to tumors located near the surface or to irradiating internal organs during an operation. For many deep-lying tumors, it is better to use epithermal neutrons in the energy range 1 eV-10 keV whose penetration power is much higher. Moderated in the tissue to thermal energy, they permit neutron-capture therapy on tumors located at depths up to 10 cm. Here it is important that the number of fast neutrons in the epithermal-neutron spectrum, which limit the possible achievable therapeutic dose in the tumor, be small. As a rule, the maximum admissable radiation load in the outer layers, which is produced by fast neutrons, is a limitation. Epithermal-neutron beams with dimension 10 × 10 cm and flux densitỹ 10 9 sec -1 ·cm -2 are needed to perform clinical studies and treatment. Several facilities where the spatial-energy formation of the epithermal-neutron beam is performed with a complicated system of moderators, filters, collimators, and shielding have now been developed on the basis of nuclear reactors [1][2][3][4]. A epithermal neutron beam with the best characteristics for neutron-capture therapy today has been produced on the basis of the 5-MW MITR II reactor (USA) [2][3][4]. In this facility, the reactor thermal-neutron flux is converted by a 235 U converter into a fission-neutron flux from which the epithermal-neutron beam is then formed. Although the nuclear reactor as an intense neutron source for radiotherapy possesses important advantages, such as high neutron flux density in space and time, the development of a series of such facilities for wide application is unrealistic even in large oncological centers because of nuclear-safety considerations, high capital costs, and operational longevity.In this connection, the development of a neutron source for neutron-capture therapy based on an inexpensive proton accelerator with energy 2-3 MeV with beam power 10-20 kW, intended for use in oncological clinics, has been widely discussed and investigated for the last 10 years [5][6][7][8]. The reaction 7 Li(p, n)...