A main challenge in modern aeronautics is to achieve disruptive design solutions for a greener and affordable aviation. One way towards this target is to increase aerodynamic efficiency through very high wing aspect ratios, involving lighter and flexible structures to reduce weight. A main obstacle in this path is to provide trustable predictions at the early design stage, where the conventional approaches fail due to insufficient knowledge, and limited room for high-fidelity analyses. Considerable progress has already been achieved by embedding more efficient, physics-based methods into the process. However, in most cases the effort of studying complex phenomena is not accompanied by an assessment of the inherent uncertainty. And yet, uncertainty can be critical especially in early design, as its negative realization in the advanced phases may produce serious consequences (such as the need to fully redesign the aircraft). The aim of this project is therefore to address this gap, by developing some suitable analysis tools in support of the conceptual design of highly flexible aircraft, with the capability of propagating some relevant uncertainty through the optimization process and finally provide information on the reliability of the results. To this end, we leverage physics-based simulation as the most complete source of information, capable of capturing non-linearities and complex disciplinary interactions typical of flexible airplane dynamics. The project is built around four objectives: 1) the development of a set of adequate models for aerodynamics, flight dynamics and structural dynamics; 2) the integration of the above modules with an aircraft sizing tool to broaden the design exploration capabilities by taking into account discipline-related uncertainty and constraints; 3) the expansion of the analysis capabilities and set of constraints by enabling coupled aero-structural analyses under uncertainty; 4) the demonstration of a robust design and optimization process for a highly flexible aircraft concept. After a detailed discussion of the background and relevant literature, this document continues presenting and discussing the development, validation and integration of the different analysis tools. Then, it introduces a first application where some of the analysis and simulation capabilities are exploited for an aircraft multi-disciplinary design & optimization process, where uncertainty is allowed to be propagated into some key performance indices. A second, more complex architecture is subsequently presented, where static and dynamic aeroelasticity is taken into account, with and without uncertainty. Finally, some studies are performed demonstrating how the proposed framework can be successfully employed in a robust analysis and optimization process of high-aspect-ratio flexible aircraft. Conclusions and future perspectives are then elaborated in the final chapter.