In this investigation, the Flexible String Algorithm (FSA), used before for 2D subsonic ducts inverse design, is developed and applied to inverse design of supersonic ducts with and without normal shock wave. In this method, the duct wall shape is changed under an algorithm based on deformation of a virtual flexible string in a flow. The deformation of the string due to the local flow conditions resulting from changes in wall geometry is performed until the target shape satisfying the prescribed walls pressure distribution is achieved. The flow field at each step is analyzed using Euler equations solutions by the AUSM method. Some validation test cases and design examples in subsonic and supersonic regimes are presented here which show the robustness and flexibility of the method in handling the complex geometries in various flow regimes. In the case of unsymmetrical ducts with two unknown walls, the FSA has been modified to increase the convergence rate significantly. Also, effect of boundary conditions at the duct inlet and outlet on convergence of FSA is investigated. The FSA is a physical and quick converging approach and can efficiently utilize flow analysis codes as a black box.