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Design of an engineering system is often a challenging task due to its multidisciplinary nature and complexity. This is further complicated due to the presence of uncertainty. In this dissertation, design is viewed as a target-driven process involving target setting and further cascading throughout a complex system. Computational methods are developed in this work for sensitivity analysis, setting flexible design targets, and probabilistic target cascading to help designers make informed decisions in design of engineering systems under uncertainty. The developed methods emphasize accommodating various sources of uncertainty and facilitating multidisciplinary design. To manage the complexity of a probabilistic design problem, statistical sensitivity analysis (SSA) and its role in engineering design are examined. A new SSA method based on the concept of the relative entropy is developed with the flexibility to be applied under various design scenarios and at various design stages. The developed method is compared with three existing SSA approaches. This comparison study provides guidelines for designers to choose a proper method for a specific design purpose. To accommodate uncertainty in setting proper design targets, a new method is developed for setting ranged sets of targets that meet design criteria while incorporating design heterogeneity information. A measure of the design heterogeneity and a metric of design flexibility are developed. The developed method helps preserve the design freedom for downstream activities and can ultimately enhance the capability of a system to be adapted to changes in a design process. To further cascading targets while incorporating uncertainty for design subproblems throughout a multilevel hierarchical system, a generalized formulation of Probabilistic Analytical Target Cascading (PATC) is developed. Several implementation issues are investigated, including representations of probabilistic design targets, meeting design consistency under uncertainty among coupling subproblems, and coordination strategies for multilevel design optimization. A particular PATC that matches mean and variance of random variables is exercised. Through various example problems, it is illustrated that the research developments in this dissertation are generally applicable to various engineering applications, thus providing intelligent computational techniques to facilitate design of complex engineering systems under uncertainty.