The objective of this paper was to investigate the impact of two commonly used turbulence models in Reynolds-averaged Navier–Stokes simulations (Spalart–Allmaras and Menter's shear stress transport models) on the three-dimensional optimum wing design obtained with the gradient-based deterministic and robust aerodynamic shape optimization in transonic, viscous, turbulent flow. In particular, the main contribution of this study to aerodynamic design area is to evaluate the impact of turbulence models and different weight distributions in the multi-objective function (equal, mean biased, and variance biased) on the computational cost, optimal shape, and its performance under Mach-number uncertainty obtained with robust optimization. The results of the study show that the effect of weight distribution in the objective function is more significant than the effect of turbulence model on the final shape obtained with robust design at lower off-design Mach numbers. Robust design tends to mitigate the impact of the turbulence model selection on the optimum shape and performance over the uncertain Mach-number range, whereas the choice of the turbulence model becomes significant at off-design conditions for the optimal shapes obtained with deterministic design. This study also demonstrates the effectiveness of using stochastic expansions in robust aerodynamic shape optimization of three-dimensional wings.