The penetration of unidirectional (UD) and [0#/90#] cross-ply ultra-high molecular weight polyethylene fibre composites by sharp-tipped cylindrical punches has been investigated. While the measured penetration pressure for both composite types increased with decreasing punch diameter, the pressure was significantly higher for the cross-ply composites and increased with decreasing ply thickness. A combination of optical microscopy and X-ray tomography revealed that in both composites, the sharp-tipped punch penetrated without fibre fracture by the formation of mode-I cracks along the fibre directions, followed by the wedging open of the crack by the advancing punch. In the cross-ply composites, delamination between adjacent 0# and 90# plies also occurred to accommodate the incompatible deformation between plies containing orthogonal mode-I cracks. Micromechanical models for the steadystate penetration pressure were developed for both composites. To account for material anisotropy as well as the large shear strains and fibre rotations, the deformation of the composites was modelled via a pressure-dependent crystal plasticity framework. Intra and inter-ply fracture were accounted for via mode-I and delamination toughnesses respectively. These models account for the competition between deformation and fracture of the plies and accurately predict the measured steady-state penetration pressures over the wide range of punch diameters and ply thicknesses investigated here. Design maps for the penetration resistance of cross-ply composites were constructed using these models and subsequently used to infer composite designs that maximise the penetration resistance for a user prescribed value of fibre strength.