A finite element code has been developed for the prediction of the radiated acoustic field from the aft fan duct of a turbofan engine. The acoustic field is modelled based on the assumption that the steady flow in and around the nacelle is irrotational as is the acoustic perturbation. The geometry of the nacelle is axisymmetric and the acoustic source is harmonic and decomposed into its angular harmonics. The steady flow is computed on the acoustic mesh and provides data for the acoustic calculations. The jet is included in the steady flow potential flow model by separating the interior and exterior flow outside the aft fan duct with a thin barrier created by disconnecting the computational domain. The jet and exterior flow are allowed to merge at a defined distance downstream. In the acoustic radiation model continuity of acoustic particle velocity is implicitly satisfied across the shear layer by careful treatment of the surface integral which appears in the finite element method (FEM) formulation. Pressure continuity is enforced by using a penalty constraint on the shear layer. A model for locally reacting acoustic treatment provides a boundary condition on the duct walls. An attempt has been made to limit reflections on the artificial baffle introduced to limit the computational domain, but this is only moderately successful. An old, but reliable frontal solution routine has been updated with considerable impact on computational time. Example calculations are given which show the success achieved in satisfying the complicated interface conditions on the shear layer and the characteristics of the solutions at relatively high frequencies where the refinement of the mesh becomes a limiting consideration for practical computations.