This paper studies optimal shape design of pressure vessel head subject to internal uniform pressure.The optimization aims at minimizing its maximum stress while the volume of the vessel head remains no less than the standard ellipsoidal head.Super-ellipse curve is selected to describe the middle surface shape of the vessel head because it represents a large family of curves with only two or three parameters and makes the design and manufacture easy.The performance of different elements and element sizes of FEM modeling is carefully studied in view of computational cost,accuracy and noises of von Mises stress.The response surface of the maximum stress vs.shape design parameters is approximated by a Kriging surrogate model with EI criterion for sampling adding,based on the parameter optimization which is carried out to search the optimal shape.Finally,it is shown by numerical comparison that the super-ellipsoidal head is better than the standard ellipsoidal head and the other vessel heads in the literature. This paper studies optimal shape design of pressure vessel head subject to internal uniform pressure. The optimization aims at minimizing its maximum stress while the volume of the vessel head remains no less than the standard ellipsoidal head. Super-ellipse curve is selected to describe the middle surface shape of the vessel head because it represents a large family of curves with only two or three parameters and makes the design and manufacture easy. The performance of different elements and element sizes of FEM modeling is carefully studied in view of computational cost, accuracy and noises of von Mises stress.The response surface of the maximum stress vs.shape design parameters is approximated by a Kriging surrogate model with EI criterion for sampling adding, based on the parameter optimization which is carried out to search the optimal shape. Finally, it is shown by numerical comparison that the super-ellipsoidal head is better than the standard ellipsoidal head and the other vessel hea ds in the literature.