This thesis concerns the computational modelling of low pressure (LP) steam turbine exhaust hood flows. A test case for LP last stage blades (LSBs) with a full aerodynamic definition and an accompanying exhaust hood was developed which is representative of current industrial practice. The test case geometry is freely available allowing other researchers to build on this work and is the first of its kind. Studies on this Durham Stage and Exhaust Hood Test Case showed the geometry produces a representative flow pattern and performance metrics comparable to other published research. Using the test case, the effect of condenser cooling water pressure gradient on the hood flow was computed for the first time. A generic boundary condition was developed to represent the transverse condenser cooling water flow and, when applied to the test case, was shown to have a larger influence on the flow asymmetry within the hood than the tip leakage jet. This thesis describes the first application of the non-linear harmonic (NLH) method to couple the LSBs to the exhaust hood. This method enabled the circumferential non-uniformity which develops in the exhaust hood to be transferred across the interface to the stage, in half the computational demand of the full annulus frozen rotor approach. The first review of the influence of inlet circumferential asymmetry on the hood flow field highlighted that modelling its effect is not as crucial as indicated in the literature, unless the diffuser axial length is very compact or if off-design flows are to be studied. A series of recommendations and guidelines for the CFD modelling of steam turbine exhaust hood flows based on this work are supplied. Experimental validation of the Durham Stage and Exhaust Hood Test Case and a comparison of full unsteady studies with the NLH method should be the next steps in this research