The critical angle for flame deflection in fires in inclined trenches was determined using the Computational Fluid Dynamics (CFD) code FLOW3D. The trenches had rectangular cross-sections and contained rectangular burners which extended the full width of the trench. Both two and three-dimensional simulations were carried out. The flowfield was simulated transiently and allowed to develop towards a final steady state. The critical angle was independent of the heat release rate. The three-dimensional simulations gave critical angles close to those measured in experiments. The critical angle was dependent on the geometry of both the trench and the burner. Longer, thinner burners and/or higher trench walls reduced the critical angle towards the value of 10 degrees determined for two-dimensional simulations. Square trenches with square burners had a critical angle of approximately 25 degrees. The critical angle was dependent on the trench and burner geometries through their effect on the shape of the plume within the trench.