Here, this study introduces a multistage mixed integer modeling framework for long-term strategic planning of the battery electric vehicle (BEV) inter-city fast charging infrastructure. In response to the growing BEV inter-city travel demand, the framework integrates both an optimization model for decisions on where and when to build charging stations and a stochastic queuing model to determine how many chargers are needed for each station. A genetic algorithm based heuristic method is developed to efficiently solve the problem. The model is applied to investigate the long-term infrastructure requirement in the state of California where significant growth in BEV demand is expected in coming decades. Our findings indicate that the charging infrastructure is expanded in both network coverage (number of stations) and service capacity (number of chargers per station) as the BEV demand grows. We also found that the infrastructure requirement is dependent on many factors, such as the BEV electrified range, the required level of service at charging stations, and the range anxiety cost. For most simulated scenarios, the results show that it is beneficial to invest in the inter-city fast charging infrastructure, even though the range anxiety cost is at its low end.