Non-reflective boundary conditions for prediction of acoustic tones in non-uniform mean flow for ducted flows New Non-Reflective Boundary Conditions (NRBC) are developed and validated for computational fluid dynamics (CFD) prediction of acoustic noise at discrete frequencies in ducts containing non-uniform mean flow. The new boundary conditions are implemented in a commercial time-unsteady CFD solver and validated in uniform and non-uniform mean flow over a range of wavenumbers and frequencies in two and three dimensions. A literature review is provided, discussing the ideas and state-of-the-art in non-reflecting boundary treatments. The test calculations are repeated with a subset of the treatments most commonly used in acoustic CFD calculations to allow comparison to be made with the current method. The primary target of the work is the prediction of acoustic tones in turbomachinery, and a final demonstration is performed for an acoustically representative test case modelling the generation and propagation of vortex/stator interaction tones. In addition to accommodating fully non-uniform (circumferentially as well as radially) mean flow the new boundary conditions are able to accommodate non-uniform duct geometries, including non-planar bounding surfaces at inlet and exit, although these capabilities have not yet been demonstrated. A discussion is provided of the results of the test calculations and it is concluded that the new boundary conditions offer the best overall capability of the methods tested for the target calculation type, with reflection coefficients of around -40dB and -20dB at the inlet and outlet boundaries respectively. Recommendations are given for future work.