A method is presented to predict the far-field sound pressure levels from the fan exhaust. The levels are found based on a known source distribution of the acoustic pressure and velocity perturbations inside the exhaust fan duct. This source distribution is propagated through the fan exhaust shear layer to a porous Ffowcs Williams-Hawkings surface using the linearized Euler equations. The linearized Euler equations are discretized in the frequency domain with the Streamline Upwind Petrov Galerkin method on an unstructured grid and are solved in parallel. This technique enables a stable numerical solution of the linearized Euler equations to be obtained. Results are shown for the Source Diagnostics Test which has a realistic engine geometry and a high speed fan-exit ow with fan tones at a relatively high frequency. Comparisons are made between the predicted and measured far-field sound pressure levels at twice the blade passage frequency.