The accelerator driven fast neutron sources of the white- and quasi-monoenergetic spectra are operated at the NPI Rez Fast Neutron Facility utilizing the Be(thick), D2O(thick), and 7Li(C) target stations and the variable energy proton beam (up to 37 MeV) from the U-120M isochronous cyclotron. Recently, the design of beryllium target station was upgraded in order to provide the higher neutron flux at the modified positions of irradiated samples. Afterwards, the thick target neutron field of the p+Be source reaction was investigated for proton energy of 35 MeV. The spectral neutron flux for several target-to-sample distances was determined using the multi-foil activation technique. From measured reaction rates, new neutron spectra were reconstructed employing the SAND-II unfolding code and validated against the MCNPX predictions. The IFMIF-like (International Fusion Material Irradiation Facility) neutron field obtained from the p(35)+Be source is suitable for the neutron cross-sections validation within the IFMIF research program, radiation hardness tests of electronics, and neutron activation analysis experiments.