A simple computer model of the Joint European Torus (JET) tokamak has been constructed, using the neutron transport code McBEND, to assist in the interpretation of point neutron source data used for empirical calibrations of fission chambers placed near the tokamak to measure the total neutron emission from deuterium and deuterium-tritium plasmas, A satisfactory simulation of the experimental data using a 252Cf neutron source is obtained. In particular, the preferential moderation and absorption of 252Cf neutrons, compared with plasma neutrons, resulting from the buildup of equipment around the tokamak in recent years is demonstrated; this differentiation between neutron sources is a consequence of the use of a concrete filler in the spaces between the toroidal field (TF) coils. An unexpected increase in detector response is explained by the substitution of Freon for water as the TF coil coolant. Finally, the McBEND calculations are found to predict correctly the relative responses of both 235U and 238U fission chambers to 2.5- and 14-MeV plasma neutrons.