It is well known that neutrons have more damaging effects, with high relative biological effectiveness or a radiation weighting factor depending on neutron energy, compared to low-LET ionizing radiations. In the current work, we evaluated the contribution of the indirect effect induced by radicals for the purpose of studying the mechanisms of fast neutron effects or mechanisms of boron neutron capture therapy (BNCT) using relatively lower energy neutrons. Plasmid pBR322 DNA with a supercoiled structure was irradiated with fast neutrons (1–10 MeV) in the reactor core of the YAYOI research reactor at the University of Tokyo, and with thermalized neutrons passing through a phantom made of acrylic resin to simulate a human body. The singleand double-strand breaks (SSBs and DSBs) of the plasmid were evaluated from the numbers of its open circular and linear forms, respectively, detected using agarose gel electrophoresis. The number of supercoiled forms decreased exponentially with the absorbed dose of fast neutrons. The decrease was inhibited by dimethyl sulfoxide (DMSO) in a concentration-dependent manner. The contributions of the indirect effect to DNA strand breaks by fast neutrons and thermalized neutrons were calculated to be 50–65% which, while lower than the value for X rays, still accounts for the majority of the DNA strand breaks. In the case of thermalized neutrons, SSB and DSB yields were increased by the addition of boric acid. Moreover, an increased 10B isotope concentration was found to increase the DSB/SSB ratio.