A general inverse design procedure has been developed to use optimization techniques and generic surface descriptions for the purpose of aerodynamic shape design. A variety of flow regimes are examined from 2-D inviscid, subsonic cases to 3-D turbulent, supersonic problems. Surface descriptions have been generalized through the use of B-splines to model a variety of curves and shapes with a minimum of parameters. The process uses a computational fluid dynamics program, GASP (the General Aerodynamic Simulation Program), and several iterative and optimization techniques to examine bodies of interest. A 2-D inviscid, subsonic airfoil test case demonstrates the ability of the procedure to solve problems governed by elliptic equations. A 3-D, viscous, compressible flow over a forebody/canopy model of a supersonic fighter and its comparison to test data establishes the ability of the method to solve practical problems of interest. Several other test cases are performed, including an axi-symmetric power law body and a 3-D elliptic cone. Unconstrained multi-parameter optimizations have been quite successful in matching target pressure coefficients and reproducing target body shapes. / Ph. D.