The development of a distributed source model to predict fan tone noise levels of an installed turbofan aero-engine is reported. The key objective is to examine a canonical problem: how to predict the pressure field due to a distributed source located near an infinite, rigid cylinder. This canonical problem is a simple representation of an installed turbofan, where the distributed source is based on the pressure pattern generated by a spinning duct mode, and the rigid cylinder represents an aircraft fuselage. The radiation of fan tones can be modelled in terms of spinning modes. In this analysis, based on duct modes, theoretical expressions for the near-field acoustic pressures on the cylinder, or at the same locations without the cylinder, have been formulated. Simulations of the near-field acoustic pressures are compared against measurements obtained from a fan rig test. Also, the installation effect is quantified by calculating the difference in the sound pressure levels with and without the adjacent cylindrical fuselage. Results are shown for the blade passing frequency fan tone radiated at a supersonic fan operating condition.