For the next generation of fusion reactors, tritium inventory will be one of the greatest safety concerns. Both CIT and ITER call for the use of graphite or carbon composites as the first wall and divertor material. If this graphite should contain a large number of traps for the storage of tritium, the resulting inventory could restrict the operation of the reactor. This report presents the results of an experimental study on the effects of neutron irradiation on the trapping of tritium in graphite. Enhancements in the trapping levels by two orders of magnitude up to as high as 0.2 atomic percent were seen for graphite samples irradiated to approximately 10 dpa at different temperatures. The results are compared to those obtained for ion damaged samples. The implications of the results for the operation of CIT and ITER are examined.