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Two- and three-dimensional surface normal grids are generated in Cartesian coordinates around a supersonic/hypersonic waverider configuration using parabolic partial differential equations. The elliptic partial differential equations for grid generation are parabolized in the xi direction in two dimesions, and in the xi and zeta directions in three dimensions. This is consistent with spatial marching flow solutions. The parabolized grid equations march in the xi direction for two dimensions and in both the xi and zeta directions for three dimensions, without iteration. The following problems are investigated: describing the boundary points, generating grids around the waverider's wing tip, using approximations to the elliptic grid generation equations too far downstream around a convex corner, and grid crossover in concave regions when orthogonality is specified. The degree of grid smoothing in the marching directions is related to the positioning of the approximations to the elliptic grid generation equations. Highly stretched surface orthogonal grids are accurately and efficiently generated without grid embedding for high Reynold's number flows. Keywords: Grids; Fluid mechanics; Navier Stokes equations; Three dimensional flow; Thesis.