Besides commercial and military applications, unmanned aerial vehicles (UAVs) are now used more commonly in disaster relief operations. This study proposes a novel model for proactive and reactive planning (different scenarios) that allow for a higher degree of realism, thus a higher likelihood for a mission of being executed according to the plan even when weather forecasts are changing. The novelty of this study results from the addition of a function of resistance of UAVs mission to changes in weather conditions. We link the influence of weather conditions on the UAV’s energy consumption. The goal is to ensure the completion of planned deliveries by a fleet of UAVs under changing weather conditions before their batteries discharge and to identify the emergency route for returned if the mission cannot be completed. An approach based on constraint programming is proposed, as it has proven to be effective in various contexts, especially related to the nonlinearity of the system’s characteristics. The proposed approach has been tested on several instances, which have allowed for analyzing how the plan of mission is robust to the changing weather conditions with different parameters, such as the fleet size, battery capacity, and distribution network layout.