Increasing environmental considerations force the logistics sector to develop more environmentally friendly approaches. Thus, the concept of "green logistics" is becoming more crucial. The use of electric vehicles, which become prominent with their low energy consumption, less cost and environmentally friendly features, is a part of green logistics. Moreover, taking into consideration of multi-echelon distribution networks can also be effective in reducing the negative outcomes of urban logistics. In this context, the Two-Echelon Electric Vehicle Routing Problem with Battery Swapping Station (2E-E-VRP-BSS) is considered in this study. A Mixed Integer Programming (MIP) model is presented for the problem in which the total cost consisting of fixed cost, transportation cost, battery swapping cost and handling cost is minimized. To test the validity of the model, three different data sets, each of different sizes, simulating a realistic distribution network were created. In addition, sensitivity analyses were carried out in order to examine the impact of changes in customer demand and battery capacities of electric vehicles on optimal solutions. The analyses indicate the applicability of the model. The findings suggest that fluctuations in customer demand directly impact the total cost, with higher demand leading to increased costs and lower demand resulting in cost reductions compared to the base case scenario. Furthermore, there is a negative correlation between the battery capacity of electric vehicles and the total cost, meaning that as battery capacity increases, the overall cost tends to decrease.