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The proposed work demonstrates the results of creating and investigating the mathematical model of the source of fast neutrons. Computer modeling of the energy spectrum of fast neutrons was carried out for 239PuBe neutron source. The model of the source of fast neutrons has been developed. Neutrons in this model have an energy spectrum from 100 keV to 11 MeV with 100 keV step. Simulation is performed by the Monte-Carlo method. The model carrier is a computer program developed in the C++ programming language in the Linux operating system environment, using the Geant4 toolkit. All necessary classes describing low-energy models were used for the simulation of the passage of neutrons through materials of detectors. Those take into account the elastic scattering, inelastic scattering, radiative capture and fission. We consider these processes because models of processes implemented in our software will be also used for other problems of neutrons transport, for example, for passing neutrons through various substances, and for conducting virtual laboratory works. The PhysicsList class of our program contains classes G4NeutronHPElastic, G4NeutronHPElasticData, G4NeutronHPInelastic, G4NeutronHPInelasticData, G4NeutronHPCapture, G4NeutronHPCaptureData, etc. based on the NeutronHP model for neutron interactions at low energy, as well as the neutron data library G4NDL4.5. Diagrams containing energy spectra of a source of fast neutrons modeled in two ways are presented in the paper. The analysis of the obtained energy spectra is carried out. Virtual nuclear physics experiments are carried out with the aim of testing the elaborated neutron-matter interaction model. The processes occurring in scintillator substances during the passage of fast neutrons through them, have been studied. 109 neutrons were used as primary particles emitted isotropically, and we used our simulation results of 239PuBe neutron source to describe the initial energy spectrum. The created model of 239PuBe neutron source can be used for the investigation of scintillation detectors Bi4Ge3O12, CdWO4, Gd2SiO5 and others, as well as studying their characteristics. Processes in heavy oxide scintillators substance during the registration of fast neutrons can be studied using the developed model. It is shown that for registration of the flow of neutrons from 239PuBe neutron source, using Bi4Ge3O12 or CdWO4 scintillators is more preferable. Results of the virtual nuclear physical experiments satisfy the published experimental data.