The objective of this study is to identify the optimal designs of converging-diverging supersonic and hypersonic nozzles that perform at maximum uniformity of thermodynamic and flow-field properties with respect to their average values at the nozzle exit. Since this is a multi-objective design optimization problem, the design variables used are parameters defining the shape of the nozzle. This work presents how variation of such parameters can influence the nozzle exit flow non-uniformities. A Computational Fluid Dynamics (CFD) software package, ANSYS FLUENT, was used to simulate the compressible, viscous gas flow-field in forty nozzle shapes, including the heat transfer analysis. The results of two turbulence models, k-e and k-ω, were computed and compared. With the analysis results obtained, the Response Surface Methodology (RSM) was applied for the purpose of performing a multi-objective optimization. The optimization was performed with ModeFrontier software package using Kriging and Radial Basis Functions (RBF) response surfaces. Final Pareto optimal nozzle shapes were then analyzed with ANSYS FLUENT to confirm the accuracy of the optimization process.