In this thesis we study some storage loading problems motivated from several practical contexts, under different types of uncertainty on the items’ data. To have robust stacking solutions against the data uncertainty, we apply the concepts of strict and adjustable robustness. We first give complexity results for various storage loading problems with stacking constraints, and point out some interesting settings in which the adjustable robust problems can be solved more efficiently than the strict ones. Then we propose different solution algorithms for the robust storage loading problems, and figure out which algorithm performs best for which data setting. We also propose a robust optimization framework dealing with storage loading problems under stochastic uncertainty. In this framework, we offer several rule-based ways of scenario generation to derive different uncertainty sets, and analyze the trade-off between cost and robustness of the robust stacking solutions. Additionally, we introduce a novel approach in dealing with stability issues of stacking configurations. Our key idea is to impose a limited payload on each item depending on its weight. We then study a storage loading problem with the interaction of stacking and payload constraints, as well as uncertainty on the weights of items, and propose different solution approaches for the robust problems.