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The excavation process in mechanised tunnelling consists of various technical components whose interaction enables safe tunnel driving. In reference to the existing geological and hydrogeological conditions, different types of face support principles are applied. In case of fine-grained cohesive soils, the face support is provided by Earth Pressure Balanced (EPB) machines, while the Slurry Shield (SLS) technology is adapted in medium-grained to coarse grained non-cohesive soils even under high groundwater pressure. For both machine techniques, the support medium (the excavated and conditioned soil (EPB) or the bentonite suspension (SLS)) needs to be adapted for the specific application. Within this chapter, the theoretical, experimental and numerical developments and results are presented concerning the fundamentals of face support in EPB and SLS tunnelling including the rheology of the support medium, the material transport and mixing process of the excavated soil and the added conditioning agent in the excavation chamber of an EPB shield machine as well as the constitutive models for investigations of the near field interactions between surrounding soil and advancing shield machine.