Abstarct: Therapeutic method BNCT (Boron neutron capture therapy) is effective way to eliminate some tumors. This therapy is baxsed on the reaction of and consists of two steps: The first stage is placement of boron carriers in tumor and second stage is irradiating tumor site by a neutron flow with desired energy and intensity. Products resulting from the reaction of neutrons with boron are energetic alpha and lithium ions that have short- ranges and high linear energy transfer (LET). Selection a suitable neutron source is of great importance to provide suitable neutron flow for reaction . Neutron source which is studied in this work is an accelerator baxsed neutron source of alpha – beryllium reaction. We have simulated this reaction using software LISE ++. We administered neutron spectra (which are neutrons with energies in the range of 1-10 MeV) and Gamma rays obtained from this simulation as spherical sources with radius of 1.5 cm in BSA (Beam Shaping Assembly). We simulated these spherical sources and BSA using the code MCNP. Several examples of BSA designees are done with the different materials and different thicknesses aiming to retrieve neutron flux at the exit of BSA that fulfills IAEA (International Atomic Energy Agency) requirements for a deep tumor therapy. Though the design which passes all the requirements was not achieved, there are some which are quiet close to the limits that are suitable for further optimization.