In this work, a brief review of modern approaches for shape optimization of mechanical systems is given. The developed methods and the appropriate software tool KEDRO for the design of experiments, for analysis and multiobjective robust optimization are considered and afterwards tested on the two-bar truss problem for deterministic case and case under uncertainty, and then applied to the shape optimization of the new composite pallet structure. In the first stage, the deterministic structural shape optimization problem of the pallet is solved. The FE-model of the composite pallet is considered and solved accurately as a multi-ply shell structure. The mechanical properties of the fiber-reinforced polymer material and two main operation cases of the loaded pallet are taken into account during the deterministic structural optimization procedure. Next, the same problem is considered as a non-deterministic one taking into account the possible uncertainties of the pallet supporting conditions. In both cases, the shape is defined using CAD-based NURBS curves. Due to the symmetry of the pallet design, the shape can be parameterized with a small number of parameters. Sensitivity analyses for probabilistic performances are given. Appropriate shapes of the pallet stiffness ribs are found for the best performance of the structure. The obtained results for the deterministic and uncertainty cases are compared, and an appropriate solution for the design of the pallet is proposed.