The shape optimization of the upper plenum of a pebble bed modular reactor (PBMR)-type gas-cooled nuclear reactor has been performed by using three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis and a multiobjective optimization procedure. A multiobjective genetic algorithm is used for multiobjective optimization. Two objective functions related to the uniformity of the flow distribution at the core inlet and pressure drop through the upper plenum are employed. Three geometric design variables, namely, the ratio of the thickness of the slot to the diameter of the rising channels, the ratio of the height of the upper plenum to the diameter of the rising channels, and the ratio of the height of the slot at the inlet to that at the outlet, are used for the optimization. Latin hypercube sampling is used to determine the experimental points. The response surface approximation model is used to approximate the Pareto-optimal front with three-dimensional RANS analysis using the shear stress transport turbulence model. Seven optimal shapes have been obtained using k-means clustering. From an analysis of two typical optimal designs, it is found that both of the objective functions have been improved remarkably in comparison with the reference design.