The design of supersonic flow paths for scramjet engines and high Mach number shock tunnel nozzles is complicated by high temperature flow effects and multidimensional inviscid/ viscous flow interactions. Due to these complications, design in the past has been enabled by making flow modelling simplifications that detract from the accuracy of the flow analysis. A relatively new approach to designing aerodynamic bodies, which automates design and does not require as many simplifying assumptions to be effective, is the coupling of a computational flow solver to an optimization algorithm. In this study, a new three-dimensional space-marching computational flow solver is developed and coupled to a gradient-search optimization algorithm. This new design tool is then used for the design optimization of an axisymmetric scramjet flow path and two high Mach number shock tunnel nozzles. The flow solver used in the design tool is an explicit, upwind, space-marching, finite-volume solver for integrating the three-dimensional parabolized Navier-Stokes equations. It is developed with an emphasis on simplicity and efficiency. Cross-stream fluxes are calculated using Toro's efficient upwind, linearized, approximate Riemann solver in flow regions of slowly varying data, and an Osher type solver in the remainder of the flow. Vigneron's technique of splitting the streamwise pressure gradient in subsonic regions is used to stabilise the flux calculations. A three-dimensional implementation of an algebraic turbulence model, a finite-rate chemistry model and a thermodynamic equilibrium model are also implemented within the solver. A range of test cases is performed to (1) validate and verify the phenomenological models implemented within the solver, thereby ensuring the simulation results used for design are credible, and (2) demonstrate the speed of the solver. The first application of the new computational design tool is the design of a scramjet flow path, which is optimized for maximum axial thrust at a flight Mach number of 12. The optimization of a scramjet flow path has been examined previously, however, this study differs to others published in that the flow is modelled using a turbulence model and a finite-rate chemical reaction model which add to the fidelity of the simulations. The external shape of the scramjet vehicle is constrained early on in the design process, therefore, the design of the scramjet is restricted to the internal flow path. Because of this constraint, and the large internal surface area of the combustor and the high skin friction iv within the combustor, the net calculated force exerted on the scramjet for both the initial and optimized design is a drag force. The drag force of the initial design, however, is reduced by 60% through optimization. The second application of the design tool is the wall contour of an axisymmetric Mach 7 shock tunnel nozzle, which is computationally optimized for minimum test core flow variation to a level of +/- 0.019 degrees for the flow angularity and +/- 0.26% for the Pitot pressure. The design is verified by constructing a nozzle with the optimized wall contour and conducting experimental Pitot surveys of the nozzle exit flow. The measured standard deviation in core flow Pitot pressure is 1.6%. However, because there is a large amount of experimental noise, it is expected that the actual core flow uniformity may be better than indicated by the raw experimental data. The last application of the computational design tool is a contoured Mach 7 square cross-section shock tunnel nozzle. This is a three-dimensional optimization problem that demonstrates the versatility of the design tool, since the effort required to implement the optimization algorithm is independent of the complexity of the flow-field and flow solver. Optimization results show that the variation in the test core flow properties could only be reduced to a Mach number variation of +/- 7% and flow angle variation of +/- 1.2 degrees ,for a short nozzle suitable for a shock tunnel. The magnitudes of the optimized nozzle exit flow deviations for the short nozzle and two other longer nozzles indicate that generating uniform flow becomes increasingly difficult as the length of square cross-section nozzles is reduced. Overall, the current research shows that coupling a flow solver to an optimization algorithm is an effective and insightful way of designing scramjets and shock tunnel nozzles.