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Metamodeling approach has been widely used due to the high computational cost of using high-fidelity simulations in engineering design. Interpretation of metamodels for the purpose of design, especially design under uncertainty, becomes important. The computational expenses associated with metamodels and the random errors introduced by sample-based methods require the development of analytical methods, such as those for global sensitivity analysis and uncertainty propagation to facilitate a robust design process. In this work, we develop generalized analytical formulations that can provide efficient as well as accurate global sensitivity analysis and uncertainty propagation for a variety of metamodels. The benefits of our proposed techniques are demonstrated through vehicle related robust design applications.