A conformal grid generation scheme has been developed and is automated in a general purpose code which can be used for the generation of computational grids for complex geometries. The code uses the repetitive application of a general analytical mapping function known as the Karman-Trefftz equation. This program can generate highly orthogonal grids having virtually any internal structure desired by the user. The only input attributes required by the program are the body coordinates of the shape, the orthogonality requirement of the grid, and information concerning the physical structure of the grid. Computational grids generated by this program are especially well suited for the numerical computation of supersonic flow fields.