The paper provides an analysis of the impact of the values of cutting tool inclination strategies and angles measured in the parallel and perpendicular to feed direction, radial depth of cut and feedrate on the surface roughness. The workpiece was made of the AISI H13 steel, hardness 50 HRC, and was machined using a ball-nosed end mill with CBN edges. The research methodology involved experiments conducted based on the Taguchi orthogonal array, optimization of parameters with the use of Taguchi method and process modelling using neural networks. Thanks to the use of neural networks, the analyses were performed for various levels of machining efficiency, obtained as a result of different radial depths of cut and feedrates. In order to obtain mathematical models well-describing strongly nonlinear impact of the cutting tool inclination strategies and angles, a separate neural network learned for each tool inclination strategy. The prediction of results was made using a set of neural networks. The analyses and experiments resulted in surfaces with very low Ra parameter of 0.16 μm and mathematical models with a good fit to the experimental data. Values of the cutting tool inclination angle that allow obtaining the surface of specific surface roughness were specified for various levels of machining performance.