A detailed model of the Target Bay (TB) at the National Ignition Facility (NIF) has been developed to estimate the post-shot radiation environment inside the facility. The model includes large number of structures and diagnostic instruments present inside the TB. These structures and instruments are activated by the few nanosecond pulse of neutrons generated during a shot and the resultant gamma dose rates are estimated at various decay times following the shot. The results presented in this paper are based on a low-yield D-T shot of 1016 neutrons. General environment dose rates drop to below 3 mrem/h within three hours following a shot with higher dose rates observed at contact with some of the components. Dose rate maps of the different TB levels were generated to aid in estimating worker stay-out times following a shot before entry is permitted into the TB.