Hypersonic airbreathing engines offer great potential for reliable and economical access-tospace and high-speed atmospheric cruise for both civilian and strategic applications. Scramjet (supersonic combustion ramjet) propulsion, in particular, is a promising technology to materialize efficient and flexible transport systems by removing the need to carry oxidizers and other limitations of rocket engines. In the actual development procedure of aerospace applications, the design for fabrication is carefully determined in consideration of various requirements and criteria, based on the optimal results obtained in numerical analysis and experiments. This stage typically involves a significant amount of engineering activities and human-related factors, which may well give rise to unexpected errors, uncertainty, and accuracy loss in the design values. Discrepancies in the design between the numerical/analytical solutions and the actual product can also arise during operation, originating from various factors such as structural deformation due to aerodynamic loads and surface ablation due to aerothermal heating in hypersonic flight. It is desirable that such discrepancies do not drastically affect the performance of the design. In this work, we present our findings of Multi-objective robust design optimization of the nozzle and external contour of an axisymmetric scramjet. We analyze the effect that uncertainties in the design variables can have on the final solutions and try to understand the behavior from the physical point of view.