Inverse design is one of the design methods of aerodynamic ducts such as S-duct intakes. In these problems, the geometry of the duct is unknown but the pressure distributions along the walls are given. In this paper, a new inverse design method called “flexible string method” is introduced. In this method, the duct walls are modified from initial guess to final shape based on the flexible string movement algorithm according to pressure distribution. In 3D design, the duct design process starts with a 2D one. At first step, a 2D Jet-Engine S-shaped air intake considering flight mach number is designed using the inverse design method based on an Euler flow solver (with no considering the jet nose engine effects). At the second step with considering duct sections like circle, ellipse and bean the 2D duct is modified to obtain the 3D duct. Finally, it is validated by analyzing the duct flow in 3D turbulent regime. The numerical studies show in spite of severe height change with respect to duct length, there is no separation in the duct and the uniformity of flow at the duct exit is completely satisfactory.