Fused filament fabrication of thermoplastic polyurethanes (TPUs) offers a capability to manufacture tailorable, flexible honeycomb structures which can be optimised for energy absorbing applications. This work explores the effect of a range of grading methodologies on the energy absorbing and damping behaviour of flexible TPU honeycomb structures. By applying density grading, the energy absorbing and damping profiles are significantly modified from the uniform density equivalent. A 3D-printing procedure was developed which allowed the manufacture of high-quality structures, which underwent cyclic loading to densification without failure. Graded honeycomb architectures had an average relative density of 0.375 ± 0.05. After quasi-static testing, arrays were subjected to sinusoidal compression over a range of amplitudes at 0.5 Hz. By grading the structural density in different ways, mechanical damping was modified. Cyclic compressive testing also showed how strain-softening of the TPU parent material could lead to reduced damping over the course of 50 cycles. Samples were subjected to impact loading at strain-rates of up to 51 s-1 and specific impact energies of up to 270 mJ/cm3. Lower peak loads were transferred for graded samples for the most severe impact cases. This behaviour reveals the potential of density grading of TPU structures to provide superior impact protection in extreme environmental conditions. Display omitted •Hyperplastic honeycombs with 4 density grading methodologies were produced via fused filament fabrication 3D-printing.•All thermoplastic polyurethane honeycombs were subjected to quasi-static, cyclic and high strain-rate impact analysis.•By density grading, energy absorbing and damping profiles were significantly modified from the uniform density equivalent.•Samples absorbed specific impact energies of up to 270 mJ/cm3 at strain-rates of up to 51 s−1 before recovering elastically.•Lower peak loads were transferred for graded samples for the most severe impact cases.