We applied a new nuclear reaction model that is a combination of the intra nuclear cascade model and the distorted wave Born approximation (DWBA) calculation to estimate neutron spectra in reactions induced by protons incident on 7Li and 9Be targets at incident energies below 50 MeV, using the particle and heavy ion transport code system (PHITS). The results obtained by PHITS with the new model reproduce the sharp peaks observed in the experimental double-differential cross sections as a result of taking into account transitions between discrete nuclear states in the DWBA. An excellent agreement was observed between the calculated results obtained using the combination model and experimental data on neutron yields from thick targets in the inclusive (p, xn) reaction.