A study has been carried out concerning the energy spectrum of the epithermal beam designed for boron neutron capture therapy of the LVR-15 research reactor. Monte Carlo (MC) calculations concerning radiation transport and dose distribution in water volumes of various shapes exposed to the epithermal neutron beam were developed with MC N-Particle/MC N-Particle Extended calculations. In addition to the energy spectra at various depths in a water phantom, longitudinal and transversal profiles of the fluence of neutrons above and below the cadmium cutoff (0.5 eV) have been evaluated for different shapes of the phantom. In particular, significant differences were found in the spatial distribution of neutrons for energy E < 0.5 eV. In order to confirm the reliability of simulations, a few depth profiles of neutron fluence below 0.5 eV, evaluated by means of MC calculations, have been compared with the profile of thermal neutrons obtained by means of experimental measurements. The consistency of results is good.