The changes in the critical current I/sub c/ of multifilament Nb/sub 3/Sn following several fission-reactor-neutron irradiations at approximately 60/sup 0/C have been investigated as a function of applied transverse magnetic field up to 160 kG. Increases in I/sub c/ below 10/sup 18/ n/cm/sup 2/ (E greater than 1 MeV) show a strong field dependence, relative changes being larger as the field increases. These increases are attributed to increases in H/sub c2/ brought about by irradiation-induced increases in the normal-state resistivity of the superconductor. For doses greater than 10/sup 18/ n/cm/sup 2/, sharp decreases in I/sub c/ are observed, but the behavior of I/sub c/ is qualitatively identical for all fields from 40 to 160 kG. Therefore, data obtained at the more easily attainable lower magnetic fields are directly applicable to the high-field regions in this high-fluence regime. However, for fluences below approximately 10/sup 18/ n/cm/sup 2/, magnetic-field-dependent measurements are required to determine the response of the superconductor to the neutron irradiation.