This thesis investigates the advantages and disadvantages of using probabilistic optimization methods in aircraft structural design. The necessity to achieve a design insensitive to system’s variations (robust) and less likely to fail (reliable) is addressed, in order to reduce costs and risk of accidents. Mathematical formulations of Robust Design Optimization (RDO), Reliability-Based Design Optimization (RBDO) and the hybrid Robust and Reliability-Based Design Optimization (RRBDO) are presented, highlighting the differences between the concepts of robustness and reliability. In these probabilistic formulations, uncertainties due to manufacturing tolerances and material defects are considered. Fundamentals of optimization are introduced, presenting different search methods and emphasizing the concept of multi-objective optimization.