We consider an integrated electric vehicle (EV) sharing network design problem under uncertain trip duration and energy consumption. The aim of the problem is to jointly optimize the strategic decisions of chargers’ locations and EV deployment as well as the operational decisions of trip acceptance, vehicle relocation and recharging. Our main objective is to maximize the profit of the EV sharing operator while satisfying a given service level constraint, imposing a lower bound on the proportion of accepted trips. We propose a two-stage scenario-based stochastic programming approach, leading to a deterministic equivalent formulation of the problem as a mixed-integer linear program (MILP). Our numerical experiments on randomly generated instances allow us to evaluate the value of the stochastic solution (VSS), highlighting the fact that the stochastic model outperforms the deterministic model with regard to the feasibility of the obtained solution and its profitability. We also carry out a sensitivity analysis of the VSS to show possible correlations to certain characteristics of trip demand.