Various countries and communities are defining strategic energy plans driven by concerns related to climate change and security of energy supply. Energy models are needed to support this decision-making process. The long time horizon inherent to strategic energy planning requires uncertainty to be accounted for. Most energy models available today are too complex or computationally expensive for uncertainty analyses to be carried out. This study proposes a concise multi-period Mixed-Integer Linear Programming (MILP) formulation for strategic energy planning under uncertainty. The modeling framework allows optimizing the energy system in a snapshot future year having as objective the total annual cost and assessing as well the global CO2-equivalent emissions. Key features of the model are a clear distinction both between demand and supply and between resources and technologies, a low computational time and a multiperiod resolution to account for issues related to seasonality and energy storage. The model is applied to a real case study and a Global Sensitivity Analysis (GSA) highlights the impact of uncertain parameters in energy planning.