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Reducing the noise level in the acoustic cavities is the important problem when treating inflight conditions of commercial planes or boats. Shape optimization of the acoustic cavity that will take into account the geometrical and material uncertainties, arising during the manufacturing process, is presented in this paper. The noise level is controlled by minimizing the energy density in the cavity, obtained through an energy method called Simplified Energy Method. Such formulation is based on our previous published work where transformation function mapping 3D cavity surface on a 2D domain was proposed. The optimization process directly relies on this function and thus avoids remeshing of the geometry. Robust optimization is performed using the nondominated sorting genetic algorithm (NSGA-II) together with the Kriging surrogate model. Influence of geometrical and material characteristics on the optimal solution is identified. [ABSTRACT FROM AUTHOR]