This paper presents the perforation behaviour of polyethylene terephthalate (PET) foam cored sandwich structures when subjected to quasi-static and dynamic loading at normal (0°) and oblique angles of 10° and 20°. An instrumented drop-weight hammer rig was used with fully-clamped conditions for the low-velocity impact test with impact energy of 40 J and velocity of 3.78 m/s. Meanwhile, the quasi-static indentation test was carried out using a universal testing machine via an Instron 4505, at crosshead displacement rate of 1 mm/min, with boundary conditions similar to those of the dynamic test. Results obtained showed that the normal impact generated the highest peak force for both the first and second peaks, which are associated with the damage to the top and bottom skins of the sandwich structures. Moreover, regardless of whether the test was done on the normal or inclined angles, it was observed that the dynamic loading produced higher force magnitude in comparison to those of the quasi-static response, due to the enhanced strength and stiffness of the components because of the strain rate and inertia effects. However, in terms of the damage profiles, it is evident that the maximum damage area increased with the increase inclination angle as supported by simple geometric analysis. For the oblique impact cases, the damage was due to the combined effect of tensile, compression, and shear for impact at 10°. The damage occurred as a result of pure shearing for the 20° impact case. In conclusion, the perforation behaviour at inclined angles allowed more area to be perforated in comparison to those of the normal cases.