This paper describes a methodology for the prediction of the radiation and propagation of tonal and broadband fan exhaust noise. The current studies focus on a frequency domain approach. The end goal of the research described In this paper is the solution of the linearized Euler equations (LEE) for realistic mean flows and engine geometries. In order to deal efficiently with complex engine geometries the methods are developed for unstructured grids. The Streamline Upwind Petrov Galerkin (SUPG) finite element method is used to prevent numerical instabilities when solving the LEE. To validate different elements of the methodology, several test cases have been performed and compared with benchmark analytical solutions. The propagation of fan exhaust noise is calculated for a simplified fan geometry with an absorbing liner condition. The effect of source frequency and spinning mode number are also examined.