Deployable membrane wings enable compact packaging of Mars airplanes inside an entry capsule, but their aeroelastic deformation can lead to unexpected shape changes during flight. Moreover, Martian flights are strongly influenced by wind disturbances. This study presents a robust trajectory optimization framework for a membrane-wing Mars airplane. Aerodynamic loads are evaluated through coupled computational fluid dynamics and membrane-structure simulations, and the resulting forces are integrated into a flight–aerodynamics coupled trajectory simulation. The vehicle is released vertically from a Mars entry capsule and transitions to an exploration flight via a pitch-up maneuver. We formulate a robust multiobjective optimization problem to simultaneously maximize flight duration and downrange distance. The search is performed using NSGA-II. Uncertainties are quantified using polynomial chaos expansion (PCE), considering two sources: (i) uncertainty in membrane displacement and (ii) uncertainty in wind disturbance. Robust optimization is conducted by maximizing the mean values of the objectives predicted by the PCE-based uncertainty model. The obtained Pareto-optimal set reveals the trade-off between endurance and range, and a maximum-range solution is identified. The results indicate that uncertainty associated with membrane displacement primarily affects the pitch-up maneuver, whereas wind disturbance significantly influences the final flight range. These findings highlight the necessity of incorporating aeroelastic and environmental uncertainties in trajectory design for deployable-wing Mars aircraft.