In recent years it has been shown that substantial fuel savings can be achieved in commercial aircraft by improving the aerodynamic design so as to suppress shock waves in regions of transonic flow. It is possible to reduce wave drag and shock losses by reshaping the fuselage, wings, nacelles, and pylons as well as the airfoils appearing in propellers, compressors, and turbines. Mathematical theory and computer codes have played a significant role in this development. The most familiar application of the theory is the use of shockless airfoils to design supercritical wing sections [1]. Equally important has been the introduction of computer codes to substitute for wind tunnel testing as a tool for the analysis of flows at off-design conditions [2].