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Despite the increasing use of carbon fibre reinforced plastic (CFRP) composites, titanium and aluminium alloys still constitute a significant proportion of modern civil aircraft structures, which are primarily assembled via mechanical joining techniques. Drilling of fastening holes is therefore a critical operation, which has to meet stringent geometric tolerance and integrity criteria. The paper details the development of a three-dimensional (3D) finite element (FE) model for drilling aerospace grade aluminium (AA7010-T7451 and AA2024-T351) and titanium (Ti-6Al-4V) alloys. The FE simulation employed a Coupled Eulerian Lagrangian (CEL) technique. The cutting tool was modelled according to a Lagrangian formulation in which the mesh follows the material displacement while the workpiece was represented by a non-translating and material deformation independent Eulerian mesh.