The response matrix of a Bonner sphere spectrometer was calculated using MCNP 4C and MCNPX 2.4.0 codes. As thermal neutron detector a 0.4 cm £; 0.4 cm 6LiI which is located at the center of a set of polyethylene spheres. The response was calculated for 0, 2, 3, 5, 8, 10, and 12 inches-diameter polyethylene spheres for neutrons whose energy goes from 2.50E(-8) to 100 MeV. The response matrix was calculated for 23 neutron energies, the response functions were energy-interpolated to 51 neutron energies and were compared with a matrix response reported in the literature, in this comparison both response matrices are in agreement. The main differences were found in the bare detector and are attributed to the irradiation conditions and cross sections, for the other detectors the differences are due to the cross sections libraries