This research project focussed on the low-velocity oblique impact response of glass fibre-reinforced epoxy laminates and sandwich structures with a range of polymeric cores of linear PVC and PET with nominal densities in the range of 90-140 kg/m3, conducted at normal (0°), 10° and 20° inclination angles, at energies up to 40 J. For the laminated composites and the linear PVC sandwich structures, at maximum impact energies, the damage area reduced whilst the energy absorbed increased with increasing inclination angle. Damage took the form of matrix cracking, due to bending and shear, combining with fibre fracture due to tensile loading. In the case of the higher density foam-core sandwich structures (PVC and PET), the maximum damage area occurs at 10° and less severe damage occurs at 20°, suggesting an effect of the combination of tensile, compression and shear occurred at 10°. Interestingly, the absorbed energy reduced with increasing inclination angle for these structures. The threshold energy in which visible damage occurs was observed at 14 J and 10 J for the laminated composites and sandwich structures, respectively. At higher energy levels (40 J), full perforation occurred. Contrary to the observations at relatively low energies, the PET-based sandwich structures showed increased damage with increasing inclination angle. An energy-balance model was established and used to successfully predict the maximum impact force (Pmax) values, showing good agreement with the experimental results up to the threshold energy. In addition, these findings also showed that core density has a great influence on the impact response of the sandwich structures, whereby the contact stiffness, C, and the maximum impact force (Pmax), increased with an increase in core density.