The Emergency Supplies Dispatching Problem, as an extension of Vehicle Routing Problem, is an important subject in emergency relief. In this paper, we focus on a specific kind of Emergency Supplies Dispatching Problem which considers the accessibility of vehicles and different vehicle types. In consideration of the actual conditions, the vehicle types may be various, and some emergency locations cannot be reached by certain types of vehicles due to the destruction of roads. Therefore, the problem addressed in this paper is more practical. We build a mathematical model of the Emergency Supplies Dispatching Problem which includes multiple depots and emergency locations, multiple kinds of emergency supplies and multiple types of vehicles. Then we adopt genetic algorithm to solve an example based on the model. The effectiveness of the model has been proved by analyzing the computational results.