We consider a facility location problem with uncertainty flow customers' demands, which we refer to as stochastic flow capturing location allocation problem (SFCLAP). Potential applications include siting farmers' market, emergency shelters, convenience stores, advertising boards and so on. For this dissertation, electric vehicle charging stations siting with maximum accessibility at lowest cost would be studied. We start with placing charging stations under the assumptions of pre-determined demands and uniform candidate facilities. After this model fails to deal with different scenarios of customers' demands, a two stage flow capturing location allocation programming framework is constructed to incorporate demand uncertainty as SFCLAP. Several extensions are built for various situations, such as secondary coverage and viewing facility's capacity as variables. And then, more capacitated stochastic programming models are considered as systems optimal and user oriented optimal cases. Systems optimal models are introduced with variations which include outsourcing the overflow and alliance within the system. User oriented optimal models incorporate users' choices with system's objectives. After the introduction of various models, an approximation method for the boundary of the problem and also the exact solution method, the L-Shaped method, are presented. As the computation time in the user oriented case surges with the expansion of the network, scenario reduction method is introduced to get similar optimal results within a reasonable time. And then, several cases including testing with different number of scenarios and different sample generating methods are operated for model validation. In the last part, simulation method is operated on the authentic network of the state of Arizona to evaluate the performance of this proposed framework.