The application of a boundary integral or "panel" method to duct flows is described. The method is capable of computing the three dimensional, steady state, subsonic, linearized (Prandtl-Glauert) potential flow about general configurations. The method is characterized by the application of a Dirichlet boundary condition and of "compressible" source and doublet distributions which are directly applied in the physical space. The geometry of the non-branching duct (one inflow and one outflow cross-section) may be arbitrary as long as the requirements for using the Prandtl-Glauert equation are met. A description of the method is given and three examples of application are presented with emphasis on the investigation of the conservation of mass-flow through the ducts.