The past few years have witnessed the increasing adoption of drones in various industries such as logistics, agriculture, military, and telecommunications. This paper considers a short-term post-disaster unmanned aerial vehicle (UAV) humanitarian relief application where first-aid products need to be delivered to the customer demand points. The presented problem, two-stage robust facility location problem with drones (two-stage RFLPD), incorporates the demand uncertainty using demand scenarios. This problem aims to find a location–allocation-assignment plan that has minimal two-stage total cost in the worst-case scenario of all the possible demand outcomes. Three different models of the problem are proposed, two of which incorporate a realistic UAV electricity consumption model while the last one has greater operational flexibility. The column-and-constraint generation method and Benders decomposition are used to solve the two models, and a thorough comparison among the deterministic facility location problem with drones (FLPD) models and three proposed models are also presented. Numerical analysis results show that the proposed model has significantly less average cost in the simulation runs compared to the deterministic FLPD. •This research considers an facility location problem with drones, which is one of the few researches that address FLP with drone operation.•This research uses an robust optimization approach to handle the uncertainty in customers’ demand.•The paper proposes multiple models that incorporates realistic drone’s electricity consumption function with various assumptions.•An exact column and constraints generation algorithm is proposed to solve the problem.