Unmanned aerial vehicles are applicable in a lot of areas including weather condition monitoring, surveillance, and reconnaissance. They need further development in design, especially, for the turbulent atmospheric conditions. Smart materials are considered for wing manufacturing for gust alleviation whereas membranes are found suitable for such applications, and therefore, analyzing aerodynamic properties of the membrane is important. Wind gusts create an abrupt atmospheric situation for unmanned aerial vehicles during the flight. In this study, a continuous gust profile and two types of stochastic gust models, i.e., Dryden gust model and von Karman gust model are developed to study the effects of gust load on a flexible membrane wing. One of the promising ways to reduce the effects of the gust is by using an electroactive membrane wing. A fluid-structure-interaction model by coupling the finite element model of the membrane and computational fluid dynamics model of the surrounding airflow is generated. Aerodynamic coefficients are calculated from the forces found from the numerical results for different gust velocities. A wind-tunnel experimental setup is used to investigate the aerodynamic responses of the membrane wing. Dryden gust model and von Karman gust model are found comparable with a minimum variation of magnitude in the gust velocity profile. The coefficients of lift and drag fluctuate significantly with the change in velocity due to wind gust. A validation of the fluid-structure-interaction model is performed by comparing the numerical results for the lift and drag coefficients with the experimental results. The outcome of this study contributes to better understand the aerodynamics and maneuverability of unmanned aerial vehicles in the gust environment.