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. The performance of the CEL based simulation was also benchmarked against an equivalent pure Lagrangian model (both tool and workpiece mesh deforms with the material). The geometry of commercially supplied twin-fluted twist drills utilised in experimental validation trials were imported into the model. Cutting speed (m/min)/ feed rate (mm/rev) combinations were 50/0.08 and 150/0.24 for the aluminium alloys while 10/0.07 and 30/0.21 were used when drilling Ti-6Al-4V. Predicted cutting forces from the CEL model were within 3-14% of the experimentally measured values while the simulated entrance and exit burr height deviated by 6-17.5% and 9-16% respectively, compared to experimental results. Additionally, the model indicated that hole surface residual stresses were typically compressive, with values of up to -344 and -711 MPa for aluminium and titanium workpieces respectively.