Electron Beam Melting (EBM) is a metal powder bed fusion (PBF) process in which the heat source is an electron beam. Differently from other metal PBF processes, today, EBM is used for mass production. As-built EBM parts are clearly recognisable by their surface roughness, which is, in some cases, one of the major limitations of the EBM process. The aim of this work is to investigate the effects of the orientation and the slope of the EBM surfaces on the surface roughness. Additionally, the machine repeatability is studied by measuring the roughness of surfaces built at different positions on the start plate. To these aims, a specific artefact was designed. Replicas of the artefact were produced using an Arcam A2X machine and Ti6Al4V powder. Descriptive and inferential statistical methods were applied to investigate whether the surface morphology was affected by process factors. The results show significant differences between the upward and downward surfaces. The upward surfaces appear less rough than the downward ones, for which a lower standard deviation was obtained in the results. The roughness of the upward surfaces is linearly influenced by the sloping angle, while the heat distribution on the cross-section was found to be a key factor in explaining the roughness of the downward surfaces.