As the last link in the electrical energy supply chain, distribution systems are in direct contact with consumers. Therefore, distribution system planners and operators have always paid attention to maintaining functionality while facing different events and various conditions. In regular studies, distribution system planners and operators only study credible events with known and limited consequences; and low-probability events, even with serious consequences, are not considered in these studies. In recent years, a growing rate of low-probability high-impact events, specifically extreme weather events such as tornados, hurricanes, and floods, has raised concerns over the functionality of distribution systems in confrontation with these events. Resiliency studies that tend to deal with low-probability high-impact events are used to ensure the proper functioning of distribution systems while facing these events. Therefore, a new set of distribution system planning and operation models are demanded. This research focuses on the planning of the power distribution system, intending to boost its resilience against extreme weather events. Tornado is chosen as the extreme weather event in this research, and it is assumed that distribution system poles would be damaged and go out of service while a tornado occurs. The proposed model is a static planning model for the target year, and it is assumed that the tornado will only occur once a year on average in the target year. The planning problem is modeled based on the robust approach and through a tri-level optimization problem. The first-level problem deals with construction decisions, including the hardening of distribution poles and placement of emergency distributed generation systems and electrical energy storages. The objective of the first level problem is to minimize the load shedding cost in the distribution system. The second-level problem determines the worst-case outage of distribution system sections, and its objective function is to maximize the load shedding cost. The third-level problem is dedicated to model the distribution system operation. Operation actions divide into preventive actions (prior to the tornado) and corrective actions (during the tornado). Corrective actions consist of re-dispatching the energy sources in the distribution system and charging of energy storages, while corrective actions consist of load shedding in addition to those mentioned before. Similar to the first-level problem, the objective is to minimize the load shedding cost in the third level of the problem. The resulting tri-level optimization model is solved in an iterative manner using the column-and-constraint generation algorithm implemented in GAMS software. The proposed model is then implemented on the standard 33-bus distribution test system for different case studies, each representing different scenarios that distribution system planners and operators may face in the procedure of improving distribution system resilience. Numerical results analysis proves the capability of the proposed model in boosting the resilience of the distribution system against low probability high impact events. Resilience, Distribution system planning, Robust optimization