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Indian nuclear power plants have graded engineered safety features because of which accidents with large scale consequences are highly improbable. However, regulatory requirements state the necessity of a site evacuation following a site emergency or an off-site emergency. Planning for this emergency requires allocation of evacuating vehicles. This study provides a simplified model of evacuation, with focus on minimising the travel time. The vehicle allocation was considered to be an optimisation problem. Mixed integer linear programming (MILP) was used to solve this constrained optimisation problem for a particular nuclear facility site. Different evacuation modes were formulated and the evacuation travel times for each mode were estimated. The most reasonable mode of evacuation was found to be a simultaneous supply of vehicles from vehicle depot to facilities, followed by a sequential evacuation of each facility to the exit. This solution reduces unnecessary congestion at exits and also reduces the travel time.