This paper integrates available literature and experience modeling region-level evacuations and proposes a modeling approach for evacuation from an unexpected, i.e., “no-notice,” disaster. Three possible probabilistic distributions were compared to available data for predicting how many people would decide to evacuate each hour step after a disaster’s initiation. The use of a Poisson distribution with the definitions of the variables in terms of a disaster scenario is justified. It predicts the evacuation rate for people who initiate evacuation at different times and locations after the initiation of a disaster. A delay in the start of their evacuation is based on when they learn of the event requiring evacuation and how far they are from the event. The use of the Poisson distribution is validated using data from the Fukushima Nuclear Power Plant accident of 2011. This approach can also be applied to anticipated disasters before the disaster’s initiation.